diff --git a/.gitignore b/.gitignore
index 0146aaf..13141a3 100644
--- a/.gitignore
+++ b/.gitignore
@@ -32,6 +32,7 @@ gklearn/kernels/*_sym.py
 gklearn/preimage/*
 !gklearn/preimage/*.py
 !gklearn/preimage/experiments/*.py
+!gklearn/preimage/experiments/tools/*.py
 
 __pycache__
 ##*#
diff --git a/README.md b/README.md
index 3958704..7cfdecc 100644
--- a/README.md
+++ b/README.md
@@ -10,7 +10,7 @@ A Python package for graph kernels, graph edit distances and graph pre-image pro
 ## Requirements
 
 * python>=3.5
-* numpy>=1.15.2
+* numpy>=1.16.2
 * scipy>=1.1.0
 * matplotlib>=3.0.0
 * networkx>=2.2
diff --git a/gklearn/__init__.py b/gklearn/__init__.py
index c607b26..08ca4ed 100644
--- a/gklearn/__init__.py
+++ b/gklearn/__init__.py
@@ -18,4 +18,4 @@ __date__    = "November 2017"
 # import sub modules
 # from gklearn import c_ext
 # from gklearn import ged
-from gklearn import utils
+# from gklearn import utils
diff --git a/gklearn/ged/env/common_types.py b/gklearn/ged/env/common_types.py
index 2face25..d195b11 100644
--- a/gklearn/ged/env/common_types.py
+++ b/gklearn/ged/env/common_types.py
@@ -6,12 +6,13 @@ Created on Thu Mar 19 18:17:38 2020
 @author: ljia
 """
 
-from enum import Enum, auto
+from enum import Enum, unique
 
+@unique
 class AlgorithmState(Enum):
     """can be used to specify the state of an algorithm.
     """
-    CALLED = auto # The algorithm has been called.
-    INITIALIZED = auto # The algorithm has been initialized.
-    CONVERGED = auto # The algorithm has converged.
-    TERMINATED = auto # The algorithm has terminated.
\ No newline at end of file
+    CALLED = 1 # The algorithm has been called.
+    INITIALIZED = 2 # The algorithm has been initialized.
+    CONVERGED = 3 # The algorithm has converged.
+    TERMINATED = 4 # The algorithm has terminated.
\ No newline at end of file
diff --git a/gklearn/ged/env/node_map.py b/gklearn/ged/env/node_map.py
index 4812486..dc3e3bf 100644
--- a/gklearn/ged/env/node_map.py
+++ b/gklearn/ged/env/node_map.py
@@ -39,14 +39,6 @@ class NodeMap(object):
 		return np.inf
 	
 	
-	def get_forward_map(self):
-		return self.__forward_map
-	
-	
-	def get_backward_map(self):
-		return self.__backward_map
-	
-	
 	def as_relation(self, relation):
 		relation.clear()
 		for i in range(0, len(self.__forward_map)):
@@ -77,4 +69,22 @@ class NodeMap(object):
 		
 		
 	def induced_cost(self):
-		return self.__induced_cost
\ No newline at end of file
+		return self.__induced_cost
+	
+	
+	@property
+	def forward_map(self):
+		return self.__forward_map
+
+	@forward_map.setter
+	def forward_map(self, value):
+		self.__forward_map = value	
+		
+		
+	@property
+	def backward_map(self):
+		return self.__backward_map
+
+	@backward_map.setter
+	def backward_map(self, value):
+		self.__backward_map = value	
\ No newline at end of file
diff --git a/gklearn/ged/median/median_graph_estimator.py b/gklearn/ged/median/median_graph_estimator.py
index b5a829c..03c7892 100644
--- a/gklearn/ged/median/median_graph_estimator.py
+++ b/gklearn/ged/median/median_graph_estimator.py
@@ -13,6 +13,9 @@ import time
 from tqdm import tqdm
 import sys
 import networkx as nx
+import multiprocessing
+from multiprocessing import Pool
+from functools import partial
 
 
 class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined node?
@@ -47,7 +50,9 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		self.__desired_num_random_inits = 10
 		self.__use_real_randomness = True
 		self.__seed = 0
+		self.__parallel = True
 		self.__update_order = True
+		self.__sort_graphs = True # sort graphs by size when computing GEDs.
 		self.__refine = True
 		self.__time_limit_in_sec = 0
 		self.__epsilon = 0.0001
@@ -125,6 +130,16 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 	
 				else:
 					raise Exception('Invalid argument "' + opt_val  + '" for option stdout. Usage: options = "[--stdout 0|1|2] [...]"')
+
+			elif opt_name == 'parallel':
+				if opt_val == 'TRUE':
+					self.__parallel = True
+	
+				elif opt_val == 'FALSE':
+					self.__parallel = False
+	
+				else:
+					raise Exception('Invalid argument "' + opt_val  + '" for option parallel. Usage: options = "[--parallel TRUE|FALSE] [...]"')
 	
 			elif opt_name == 'update-order':
 				if opt_val == 'TRUE':
@@ -136,6 +151,16 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 				else:
 					raise Exception('Invalid argument "' + opt_val  + '" for option update-order. Usage: options = "[--update-order TRUE|FALSE] [...]"')
 					
+			elif opt_name == 'sort-graphs':
+				if opt_val == 'TRUE':
+					self.__sort_graphs = True
+	
+				elif opt_val == 'FALSE':
+					self.__sort_graphs = False
+	
+				else:
+					raise Exception('Invalid argument "' + opt_val  + '" for option sort-graphs. Usage: options = "[--sort-graphs TRUE|FALSE] [...]"')
+					
 			elif opt_name == 'refine':
 				if opt_val == 'TRUE':
 					self.__refine = True
@@ -302,7 +327,7 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		self.__median_id = gen_median_id
 		self.__state = AlgorithmState.TERMINATED
 		
-		# Get ExchangeGraph representations of the input graphs.
+		# Get NetworkX graph representations of the input graphs.
 		graphs = {}
 		for graph_id in graph_ids:
 			# @todo: get_nx_graph() function may need to be modified according to the coming code.
@@ -312,7 +337,6 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 #		print(graphs[0].nodes(data=True))
 #		print(graphs[0].edges(data=True))
 #		print(nx.adjacency_matrix(graphs[0]))
-
 			
 		# Construct initial medians.
 		medians = []
@@ -356,30 +380,14 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			self.__ged_env.load_nx_graph(median, gen_median_id)
 			self.__ged_env.init(self.__ged_env.get_init_type())
 			
-			# Print information about current iteration.
-			if self.__print_to_stdout == 2:
-				progress = tqdm(desc='Computing initial node maps', total=len(graph_ids), file=sys.stdout)
-				
 			# Compute node maps and sum of distances for initial median.
-			self.__sum_of_distances = 0
-			self.__node_maps_from_median.clear()
-			for graph_id in graph_ids:
-				self.__ged_env.run_method(gen_median_id, graph_id)
-				self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(gen_median_id, graph_id)
-# 				print(self.__node_maps_from_median[graph_id])
-				self.__sum_of_distances += self.__node_maps_from_median[graph_id].induced_cost()
-# 				print(self.__sum_of_distances)
-				# Print information about current iteration.
-				if self.__print_to_stdout == 2:
-					progress.update(1)
-					
+# 			xxx = self.__node_maps_from_median
+			self.__compute_init_node_maps(graph_ids, gen_median_id)
+# 			yyy = self.__node_maps_from_median
+			
 			self.__best_init_sum_of_distances = min(self.__best_init_sum_of_distances, self.__sum_of_distances)
 			self.__ged_env.load_nx_graph(median, set_median_id)
 # 			print(self.__best_init_sum_of_distances)
-			
-			# Print information about current iteration.
-			if self.__print_to_stdout == 2:
-				print('\n')
 				
 			# Run block gradient descent from initial median.
 			converged = False
@@ -434,7 +442,7 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 # 					print(self.__node_maps_from_median[graph_id].induced_cost())
 # 					xxx = self.__node_maps_from_median[graph_id]					   
 					self.__ged_env.compute_induced_cost(gen_median_id, graph_id, self.__node_maps_from_median[graph_id])
-#					print('---------------------------------------')
+# 					print('---------------------------------------')
 # 					print(self.__node_maps_from_median[graph_id].induced_cost())
 					# @todo:!!!!!!!!!!!!!!!!!!!!!!!!!!!!This value is a slight different from the c++ program, which might be a bug! Use it very carefully!
 					
@@ -540,18 +548,31 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			progress.update(1)
 			
 		# Improving the node maps.
+		nb_nodes_median = self.__ged_env.get_graph_num_nodes(self.__gen_median_id)
 		for graph_id, node_map in self.__node_maps_from_median.items():
 			if time.expired():
 				if self.__state == AlgorithmState.TERMINATED:
 					self.__state = AlgorithmState.CONVERGED
 				break
-			self.__ged_env.run_method(self.__gen_median_id, graph_id)
-			if self.__ged_env.get_upper_bound(self.__gen_median_id, graph_id) < node_map.induced_cost():
-				self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(self.__gen_median_id, graph_id)
-			self.__sum_of_distances += self.__node_maps_from_median[graph_id].induced_cost()
+
+			nb_nodes_g = self.__ged_env.get_graph_num_nodes(graph_id)
+			if nb_nodes_median <= nb_nodes_g or not self.__sort_graphs:			
+				self.__ged_env.run_method(self.__gen_median_id, graph_id)
+				if self.__ged_env.get_upper_bound(self.__gen_median_id, graph_id) < node_map.induced_cost():
+					self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(self.__gen_median_id, graph_id)
+			else:
+				self.__ged_env.run_method(graph_id, self.__gen_median_id)
+				if self.__ged_env.get_upper_bound(graph_id, self.__gen_median_id) < node_map.induced_cost():
+						node_map_tmp = self.__ged_env.get_node_map(graph_id, self.__gen_median_id)
+						node_map_tmp.forward_map, node_map_tmp.backward_map = node_map_tmp.backward_map, node_map_tmp.forward_map
+						self.__node_maps_from_median[graph_id] = node_map_tmp	
+			
+			self.__sum_of_distances += self.__node_maps_from_median[graph_id].induced_cost()				
+
 			# Print information.
 			if self.__print_to_stdout == 2:
 				progress.update(1)
+
 		self.__sum_of_distances = 0.0
 		for key, val in self.__node_maps_from_median.items():
 			self.__sum_of_distances += val.induced_cost()
@@ -562,7 +583,7 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			
 	
 	def __median_available(self):
-		return self.__gen_median_id != np.inf
+		return self.__median_id != np.inf
 	
 	
 	def get_state(self):
@@ -637,7 +658,9 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		self.__desired_num_random_inits = 10
 		self.__use_real_randomness = True
 		self.__seed = 0
+		self.__parallel = True
 		self.__update_order = True
+		self.__sort_graphs = True
 		self.__refine = True
 		self.__time_limit_in_sec = 0
 		self.__epsilon = 0.0001
@@ -682,35 +705,138 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 	def __compute_medoid(self, graph_ids, timer, initial_medians):
 		# Use method selected for initialization phase.
 		self.__ged_env.set_method(self.__init_method, self.__init_options)
-		
-		# Print information about current iteration.
-		if self.__print_to_stdout == 2:
-			progress = tqdm(desc='Computing medoid', total=len(graph_ids), file=sys.stdout)
-			
+					
 		# Compute the medoid.
-		medoid_id = graph_ids[0]
-		best_sum_of_distances = np.inf
-		for g_id in graph_ids:
-			if timer.expired():
-				self.__state = AlgorithmState.CALLED
-				break
-			sum_of_distances = 0
-			for h_id in graph_ids:
-				self.__ged_env.run_method(g_id, h_id)
-				sum_of_distances += self.__ged_env.get_upper_bound(g_id, h_id)
-			if sum_of_distances < best_sum_of_distances:
-				best_sum_of_distances = sum_of_distances
-				medoid_id = g_id
-				
+		if self.__parallel:
+			# @todo: notice when parallel self.__ged_env is not modified.
+			sum_of_distances_list = [np.inf] * len(graph_ids)
+			len_itr = len(graph_ids)
+			itr = zip(graph_ids, range(0, len(graph_ids)))
+			n_jobs = multiprocessing.cpu_count()
+			if len_itr < 100 * n_jobs:
+				chunksize = int(len_itr / n_jobs) + 1
+			else:
+				chunksize = 100
+			def init_worker(ged_env_toshare):
+				global G_ged_env
+				G_ged_env = ged_env_toshare
+			do_fun = partial(_compute_medoid_parallel, graph_ids, self.__sort_graphs)
+			pool = Pool(processes=n_jobs, initializer=init_worker, initargs=(self.__ged_env,))
+			if self.__print_to_stdout == 2:
+				iterator = tqdm(pool.imap_unordered(do_fun, itr, chunksize),
+							desc='Computing medoid', file=sys.stdout)
+			else:
+				iterator = pool.imap_unordered(do_fun, itr, chunksize)
+			for i, dis in iterator:
+				sum_of_distances_list[i] = dis
+			pool.close()
+			pool.join()
+			
+			medoid_id = np.argmin(sum_of_distances_list)
+			best_sum_of_distances = sum_of_distances_list[medoid_id]
+			
+			initial_medians.append(self.__ged_env.get_nx_graph(medoid_id, True, True, False)) # @todo
+
+		else:
 			# Print information about current iteration.
 			if self.__print_to_stdout == 2:
-				progress.update(1)
-		initial_medians.append(self.__ged_env.get_nx_graph(medoid_id, True, True, False)) # @todo
+				progress = tqdm(desc='Computing medoid', total=len(graph_ids), file=sys.stdout)
 		
-		# Print information about current iteration.
-		if self.__print_to_stdout == 2:
-			print('\n')
+			medoid_id = graph_ids[0]
+			best_sum_of_distances = np.inf
+			for g_id in graph_ids:
+				if timer.expired():
+					self.__state = AlgorithmState.CALLED
+					break
+				nb_nodes_g = self.__ged_env.get_graph_num_nodes(g_id)
+				sum_of_distances = 0
+				for h_id in graph_ids:					
+					nb_nodes_h = self.__ged_env.get_graph_num_nodes(h_id)
+					if nb_nodes_g <= nb_nodes_h or not self.__sort_graphs:
+						self.__ged_env.run_method(g_id, h_id)
+						sum_of_distances += self.__ged_env.get_upper_bound(g_id, h_id)
+					else:
+						self.__ged_env.run_method(h_id, g_id)
+						sum_of_distances += self.__ged_env.get_upper_bound(h_id, g_id)	
+				if sum_of_distances < best_sum_of_distances:
+					best_sum_of_distances = sum_of_distances
+					medoid_id = g_id
+					
+				# Print information about current iteration.
+				if self.__print_to_stdout == 2:
+					progress.update(1)
+					
+			initial_medians.append(self.__ged_env.get_nx_graph(medoid_id, True, True, False)) # @todo
+			
+			# Print information about current iteration.
+			if self.__print_to_stdout == 2:
+				print('\n')
+			
 			
+	def __compute_init_node_maps(self, graph_ids, gen_median_id):
+		# Compute node maps and sum of distances for initial median.
+		if self.__parallel:
+			# @todo: notice when parallel self.__ged_env is not modified.
+			self.__sum_of_distances = 0
+			self.__node_maps_from_median.clear()
+			sum_of_distances_list = [0] * len(graph_ids)
+			
+			len_itr = len(graph_ids)
+			itr = graph_ids
+			n_jobs = multiprocessing.cpu_count()
+			if len_itr < 100 * n_jobs:
+				chunksize = int(len_itr / n_jobs) + 1
+			else:
+				chunksize = 100
+			def init_worker(ged_env_toshare):
+				global G_ged_env
+				G_ged_env = ged_env_toshare
+			nb_nodes_median = self.__ged_env.get_graph_num_nodes(gen_median_id)
+			do_fun = partial(_compute_init_node_maps_parallel, gen_median_id, self.__sort_graphs, nb_nodes_median)
+			pool = Pool(processes=n_jobs, initializer=init_worker, initargs=(self.__ged_env,))
+			if self.__print_to_stdout == 2:
+				iterator = tqdm(pool.imap_unordered(do_fun, itr, chunksize),
+							desc='Computing initial node maps', file=sys.stdout)
+			else:
+				iterator = pool.imap_unordered(do_fun, itr, chunksize)
+			for g_id, sod, node_maps in iterator:
+				sum_of_distances_list[g_id] = sod
+				self.__node_maps_from_median[g_id] = node_maps
+			pool.close()
+			pool.join()
+			
+			self.__sum_of_distances = np.sum(sum_of_distances_list)
+# 			xxx = self.__node_maps_from_median
+			
+		else:
+			# Print information about current iteration.
+			if self.__print_to_stdout == 2:
+				progress = tqdm(desc='Computing initial node maps', total=len(graph_ids), file=sys.stdout)
+				
+			self.__sum_of_distances = 0
+			self.__node_maps_from_median.clear()
+			nb_nodes_median = self.__ged_env.get_graph_num_nodes(gen_median_id)
+			for graph_id in graph_ids:
+				nb_nodes_g = self.__ged_env.get_graph_num_nodes(graph_id)
+				if nb_nodes_median <= nb_nodes_g or not self.__sort_graphs:
+					self.__ged_env.run_method(gen_median_id, graph_id)
+					self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(gen_median_id, graph_id)
+				else:
+					self.__ged_env.run_method(graph_id, gen_median_id)
+					node_map_tmp = self.__ged_env.get_node_map(graph_id, gen_median_id)
+					node_map_tmp.forward_map, node_map_tmp.backward_map = node_map_tmp.backward_map, node_map_tmp.forward_map
+					self.__node_maps_from_median[graph_id] = node_map_tmp
+	# 				print(self.__node_maps_from_median[graph_id])
+				self.__sum_of_distances += self.__node_maps_from_median[graph_id].induced_cost()
+	# 				print(self.__sum_of_distances)
+				# Print information about current iteration.
+				if self.__print_to_stdout == 2:
+					progress.update(1)
+			
+			# Print information about current iteration.
+			if self.__print_to_stdout == 2:
+				print('\n')
+
 		
 	def __termination_criterion_met(self, converged, timer, itr, itrs_without_update):
 		if timer.expired() or (itr >= self.__max_itrs if self.__max_itrs >= 0 else False):
@@ -743,6 +869,7 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		
 		
 	def __update_node_labels(self, graphs, median):
+# 		print('----------------------------')
 		
 		# Print information about current iteration.
 		if self.__print_to_stdout == 2:
@@ -750,14 +877,15 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			
 		# Iterate through all nodes of the median.
 		for i in range(0, nx.number_of_nodes(median)):
-#			print('i: ', i)
+# 			print('i: ', i)
 			# Collect the labels of the substituted nodes.
 			node_labels = []
 			for graph_id, graph in graphs.items():
-#				print('graph_id: ', graph_id)
-#				print(self.__node_maps_from_median[graph_id])
+# 				print('graph_id: ', graph_id)
+# 				print(self.__node_maps_from_median[graph_id])
+# 				print(self.__node_maps_from_median[graph_id].forward_map, self.__node_maps_from_median[graph_id].backward_map)
 				k = self.__node_maps_from_median[graph_id].image(i)
-#				print('k: ', k)
+# 				print('k: ', k)
 				if k != np.inf:
 					node_labels.append(graph.nodes[k])
 					
@@ -816,26 +944,70 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 
 
 	def __update_node_maps(self):
-		# Print information about current iteration.
-		if self.__print_to_stdout == 2:
-			progress = tqdm(desc='Updating node maps', total=len(self.__node_maps_from_median), file=sys.stdout)
-			
 		# Update the node maps.
-		node_maps_were_modified = False
-		for graph_id, node_map in self.__node_maps_from_median.items():
-			self.__ged_env.run_method(self.__median_id, graph_id)
-			if self.__ged_env.get_upper_bound(self.__median_id, graph_id) < node_map.induced_cost() - self.__epsilon:
-# 				xxx = self.__node_maps_from_median[graph_id]
-				self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(self.__median_id, graph_id)
-# 				yyy = self.__node_maps_from_median[graph_id]
-				node_maps_were_modified = True
+		if self.__parallel:
+			# @todo: notice when parallel self.__ged_env is not modified.
+			node_maps_were_modified = False
+# 			xxx = self.__node_maps_from_median.copy()
+			
+			len_itr = len(self.__node_maps_from_median)
+			itr = [item for item in self.__node_maps_from_median.items()]
+			n_jobs = multiprocessing.cpu_count()
+			if len_itr < 100 * n_jobs:
+				chunksize = int(len_itr / n_jobs) + 1
+			else:
+				chunksize = 100
+			def init_worker(ged_env_toshare):
+				global G_ged_env
+				G_ged_env = ged_env_toshare
+			nb_nodes_median = self.__ged_env.get_graph_num_nodes(self.__median_id)
+			do_fun = partial(_update_node_maps_parallel, self.__median_id, self.__epsilon, self.__sort_graphs, nb_nodes_median)
+			pool = Pool(processes=n_jobs, initializer=init_worker, initargs=(self.__ged_env,))
+			if self.__print_to_stdout == 2:
+				iterator = tqdm(pool.imap_unordered(do_fun, itr, chunksize),
+							desc='Updating node maps', file=sys.stdout)
+			else:
+				iterator = pool.imap_unordered(do_fun, itr, chunksize)
+			for g_id, node_map, nm_modified in iterator:
+				self.__node_maps_from_median[g_id] = node_map
+				if nm_modified:
+					node_maps_were_modified = True
+			pool.close()
+			pool.join()
+# 			yyy = self.__node_maps_from_median.copy()
+
+		else:
 			# Print information about current iteration.
 			if self.__print_to_stdout == 2:
-				progress.update(1)
-			
-		# Print information about current iteration.
-		if self.__print_to_stdout == 2:
-			print('\n')
+				progress = tqdm(desc='Updating node maps', total=len(self.__node_maps_from_median), file=sys.stdout)
+				
+			node_maps_were_modified = False
+			nb_nodes_median = self.__ged_env.get_graph_num_nodes(self.__median_id)
+			for graph_id, node_map in self.__node_maps_from_median.items():
+				nb_nodes_g = self.__ged_env.get_graph_num_nodes(graph_id)
+				
+				if nb_nodes_median <= nb_nodes_g or not self.__sort_graphs:
+					self.__ged_env.run_method(self.__median_id, graph_id)
+					if self.__ged_env.get_upper_bound(self.__median_id, graph_id) < node_map.induced_cost() - self.__epsilon:
+		# 				xxx = self.__node_maps_from_median[graph_id]
+						self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(self.__median_id, graph_id)
+						node_maps_were_modified = True
+						
+				else:
+					self.__ged_env.run_method(graph_id, self.__median_id)
+					if self.__ged_env.get_upper_bound(graph_id, self.__median_id) < node_map.induced_cost() - self.__epsilon:
+						node_map_tmp = self.__ged_env.get_node_map(graph_id, self.__median_id)
+						node_map_tmp.forward_map, node_map_tmp.backward_map = node_map_tmp.backward_map, node_map_tmp.forward_map
+						self.__node_maps_from_median[graph_id] = node_map_tmp	
+						node_maps_were_modified = True
+					
+				# Print information about current iteration.
+				if self.__print_to_stdout == 2:
+					progress.update(1)
+				
+			# Print information about current iteration.
+			if self.__print_to_stdout == 2:
+				print('\n')
 			
 		# Return true if the node maps were modified.
 		return node_maps_were_modified
@@ -846,6 +1018,11 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		if self.__print_to_stdout == 2:
 			print('Trying to decrease order: ... ', end='')
 			
+		if nx.number_of_nodes(median) <= 1:
+			if self.__print_to_stdout == 2:
+				print('median graph has only 1 node, skip decrease.')
+			return False
+			
 		# Initialize ID of the node that is to be deleted.
 		id_deleted_node = [None] # @todo: or np.inf
 		decreased_order = False
@@ -853,7 +1030,11 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 		# Decrease the order as long as the best deletion delta is negative.
 		while self.__compute_best_deletion_delta(graphs, median, id_deleted_node) < -self.__epsilon:
 			decreased_order = True
-			median = self.__delete_node_from_median(id_deleted_node[0], median)
+			self.__delete_node_from_median(id_deleted_node[0], median)
+			if nx.number_of_nodes(median) <= 1:
+				if self.__print_to_stdout == 2:
+					print('decrease stopped because median graph remains only 1 node. ', end='')
+				break
 			
 		# Print information about current iteration.
 		if self.__print_to_stdout == 2:
@@ -896,16 +1077,22 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 	
 	def __delete_node_from_median(self, id_deleted_node, median):
 		# Update the median.
+		mapping = {}
+		for i in range(0, nx.number_of_nodes(median)):
+			if i != id_deleted_node:
+				new_i = (i if i < id_deleted_node else (i - 1))
+				mapping[i] = new_i
 		median.remove_node(id_deleted_node)
-		median = nx.convert_node_labels_to_integers(median, first_label=0, ordering='default', label_attribute=None) # @todo:  This doesn't guarantee that the order is the same as in G.
+		nx.relabel_nodes(median, mapping, copy=False)
 		
 		# Update the node maps.
+# 		xxx = self.__node_maps_from_median
 		for key, node_map in self.__node_maps_from_median.items():
 			new_node_map = NodeMap(nx.number_of_nodes(median), node_map.num_target_nodes())
 			is_unassigned_target_node = [True] * node_map.num_target_nodes()
 			for i in range(0, nx.number_of_nodes(median) + 1):
 				if i != id_deleted_node:
-					new_i = (i if i < id_deleted_node else i - 1)
+					new_i = (i if i < id_deleted_node else (i - 1))
 					k = node_map.image(i)
 					new_node_map.add_assignment(new_i, k)
 					if k != np.inf:
@@ -913,13 +1100,12 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			for k in range(0, node_map.num_target_nodes()):
 				if is_unassigned_target_node[k]:
 					new_node_map.add_assignment(np.inf, k)
-# 			print(new_node_map.get_forward_map(), new_node_map.get_backward_map())
+# 			print(self.__node_maps_from_median[key].forward_map, self.__node_maps_from_median[key].backward_map)
+# 			print(new_node_map.forward_map, new_node_map.backward_map
 			self.__node_maps_from_median[key] = new_node_map
 			
 		# Increase overall number of decreases.
 		self.__num_decrease_order += 1
-		
-		return median
 	
 	
 	def __increase_order(self, graphs, median):
@@ -1115,10 +1301,22 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 						continue
 					for label in median_labels:
 						weights[label_id] = min(weights[label_id], self.__ged_env.get_node_rel_cost(dict(label), dict(node_labels[label_id])))
-				selected_label_id = urng.choice(range(0, len(weights)), size=1, p=np.array(weights) / np.sum(weights))[0] # for c++ test: xxx[iii] 
+				
+				# get non-zero weights.
+				weights_p, idx_p = [], []
+				for i, w in enumerate(weights):
+					if w != 0:
+						weights_p.append(w)
+						idx_p.append(i)
+				if len(weights_p) > 0:
+					p = np.array(weights_p) / np.sum(weights_p)
+					selected_label_id = urng.choice(range(0, len(weights_p)), size=1, p=p)[0] # for c++ test: xxx[iii] 
+					selected_label_id = idx_p[selected_label_id]
 # 				iii += 1 for c++ test
-				median_labels.append(node_labels[selected_label_id])
-				already_selected[selected_label_id] = True
+					median_labels.append(node_labels[selected_label_id])
+					already_selected[selected_label_id] = True
+				else: # skip the loop when all node_labels are selected. This happens when len(node_labels) <= self.__num_inits_increase_order.
+					break
 		else:
 			# Compute the initial node medians as the medians of randomly generated clusters of (roughly) equal size.
 			# @todo: go through and test.
@@ -1195,6 +1393,8 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 				 
 	
 	def __update_node_label(self, node_labels, node_label):
+		if len(node_labels) == 0: # @todo: check if this is the correct solution. Especially after calling __update_config().
+			return False
 		new_node_label = self.__get_median_node_label(node_labels)
 		if self.__ged_env.get_node_rel_cost(new_node_label, node_label) > self.__epsilon:
 			node_label.clear()
@@ -1225,7 +1425,8 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 	
 	def __add_node_to_median(self, best_config, best_label, median):
 		# Update the median.
-		median.add_node(nx.number_of_nodes(median), **best_label)
+		nb_nodes_median = nx.number_of_nodes(median)
+		median.add_node(nb_nodes_median, **best_label)
 		
 		# Update the node maps.
 		for graph_id, node_map in self.__node_maps_from_median.items():
@@ -1239,47 +1440,6 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 			
 		# Increase overall number of increases.
 		self.__num_increase_order += 1
-			
-	
-	def __improve_sum_of_distances(self, timer):
-		pass
-	
-	
-	def __median_available(self):
-		return self.__median_id != np.inf
-		
-				
-# 	def __get_node_image_from_map(self, node_map, node):
-# 		"""
-# 		Return ID of the node mapping of `node` in `node_map`.
-
-# 		Parameters
-# 		----------
-# 		node_map : list[tuple(int, int)]
-# 			List of node maps where the mapping node is found.
-# 		
-# 		node : int
-# 			The mapping node of this node is returned
-
-# 		Raises
-# 		------
-# 		Exception
-# 			If the node with ID `node` is not contained in the source nodes of the node map.
-
-# 		Returns
-# 		-------
-# 		int
-# 			ID of the mapping of `node`.
-# 			
-# 		Notes
-# 		-----
-# 		This function is not implemented in the `ged::MedianGraphEstimator` class of the `GEDLIB` library. Instead it is a Python implementation of the `ged::NodeMap::image` function.
-# 		"""
-# 		if node < len(node_map):
-# 			return node_map[node][1] if node_map[node][1] < len(node_map) else np.inf
-# 		else:
-# 			raise Exception('The node with ID ', str(node), ' is not contained in the source nodes of the node map.')
-# 		return np.inf
 				
 	
 	def __are_graphs_equal(self, g1, g2):
@@ -1489,4 +1649,61 @@ class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined no
 #			median_label = {}
 #			for key, val in median.items():
 #				median_label[key] = str(val)
-#			return median_label
\ No newline at end of file
+#			return median_label
+
+
+def _compute_medoid_parallel(graph_ids, sort, itr):
+	g_id = itr[0]
+	i = itr[1]
+	# @todo: timer not considered here.
+# 			if timer.expired():
+# 				self.__state = AlgorithmState.CALLED
+# 				break
+	nb_nodes_g = G_ged_env.get_graph_num_nodes(g_id)
+	sum_of_distances = 0
+	for h_id in graph_ids:
+		nb_nodes_h = G_ged_env.get_graph_num_nodes(h_id)
+		if nb_nodes_g <= nb_nodes_h or not sort:
+			G_ged_env.run_method(g_id, h_id)
+			sum_of_distances += G_ged_env.get_upper_bound(g_id, h_id)
+		else:
+			G_ged_env.run_method(h_id, g_id)
+			sum_of_distances += G_ged_env.get_upper_bound(h_id, g_id)
+	return i, sum_of_distances
+				
+
+def _compute_init_node_maps_parallel(gen_median_id, sort, nb_nodes_median, itr):
+	graph_id = itr
+	nb_nodes_g = G_ged_env.get_graph_num_nodes(graph_id)
+	if nb_nodes_median <= nb_nodes_g or not sort:
+		G_ged_env.run_method(gen_median_id, graph_id)
+		node_map = G_ged_env.get_node_map(gen_median_id, graph_id)
+# 				print(self.__node_maps_from_median[graph_id])
+	else:
+		G_ged_env.run_method(graph_id, gen_median_id)
+		node_map = G_ged_env.get_node_map(graph_id, gen_median_id)
+		node_map.forward_map, node_map.backward_map = node_map.backward_map, node_map.forward_map
+	sum_of_distance = node_map.induced_cost()
+# 				print(self.__sum_of_distances)
+	return graph_id, sum_of_distance, node_map
+					
+
+def _update_node_maps_parallel(median_id, epsilon, sort, nb_nodes_median, itr):
+	graph_id = itr[0]
+	node_map = itr[1]
+
+	node_maps_were_modified = False
+	nb_nodes_g = G_ged_env.get_graph_num_nodes(graph_id)
+	if nb_nodes_median <= nb_nodes_g or not sort:
+		G_ged_env.run_method(median_id, graph_id)
+		if G_ged_env.get_upper_bound(median_id, graph_id) < node_map.induced_cost() - epsilon:
+			node_map = G_ged_env.get_node_map(median_id, graph_id)
+			node_maps_were_modified = True			
+	else:
+		G_ged_env.run_method(graph_id, median_id)
+		if G_ged_env.get_upper_bound(graph_id, median_id) < node_map.induced_cost() - epsilon:
+			node_map = G_ged_env.get_node_map(graph_id, median_id)
+			node_map.forward_map, node_map.backward_map = node_map.backward_map, node_map.forward_map
+			node_maps_were_modified = True	
+			
+	return graph_id, node_map, node_maps_were_modified
\ No newline at end of file
diff --git a/gklearn/ged/median/test_median_graph_estimator.py b/gklearn/ged/median/test_median_graph_estimator.py
index 7497bab..60bce83 100644
--- a/gklearn/ged/median/test_median_graph_estimator.py
+++ b/gklearn/ged/median/test_median_graph_estimator.py
@@ -53,7 +53,7 @@ def test_median_graph_estimator():
 	mge.set_refine_method(algo, '--threads ' + str(threads) + ' --initial-solutions ' + str(initial_solutions) + ' --ratio-runs-from-initial-solutions 1')
 	
 	mge_options = '--time-limit ' + str(time_limit) + ' --stdout 2 --init-type ' + init_type
-	mge_options += ' --random-inits ' + str(num_inits) + ' --seed ' + '1'  + ' --update-order TRUE --refine FALSE --randomness PSEUDO '# @todo: std::to_string(rng())
+	mge_options += ' --random-inits ' + str(num_inits) + ' --seed ' + '1'  + ' --update-order TRUE --refine FALSE --randomness PSEUDO  --parallel TRUE '# @todo: std::to_string(rng())
 	
 	# Select the GED algorithm.
 	algo_options = '--threads ' + str(threads) + algo_options_suffix
@@ -127,7 +127,7 @@ def test_median_graph_estimator_symb():
 	mge.set_refine_method(algo, '--threads ' + str(threads) + ' --initial-solutions ' + str(initial_solutions) + ' --ratio-runs-from-initial-solutions 1')
 	
 	mge_options = '--time-limit ' + str(time_limit) + ' --stdout 2 --init-type ' + init_type
-	mge_options += ' --random-inits ' + str(num_inits) + ' --seed ' + '1'  + ' --update-order TRUE --refine FALSE'# @todo: std::to_string(rng())
+	mge_options += ' --random-inits ' + str(num_inits) + ' --seed ' + '1'  + ' --update-order TRUE --refine FALSE --randomness PSEUDO --parallel TRUE '# @todo: std::to_string(rng())
 	
 	# Select the GED algorithm.
 	algo_options = '--threads ' + str(threads) + algo_options_suffix
@@ -155,5 +155,5 @@ def test_median_graph_estimator_symb():
 
 
 if __name__ == '__main__':
- 	set_median, gen_median = test_median_graph_estimator()
- 	# set_median, gen_median = test_median_graph_estimator_symb()
\ No newline at end of file
+ 	# set_median, gen_median = test_median_graph_estimator()
+ 	set_median, gen_median = test_median_graph_estimator_symb()
\ No newline at end of file
diff --git a/gklearn/ged/median/utils.py b/gklearn/ged/median/utils.py
index 908cb11..d27c86d 100644
--- a/gklearn/ged/median/utils.py
+++ b/gklearn/ged/median/utils.py
@@ -30,8 +30,12 @@ def mge_options_to_string(options):
 			opt_str += '--randomness ' + str(val) + ' '
 		elif key == 'verbose':
 			opt_str += '--stdout ' + str(val) + ' '
+		elif key == 'parallel':
+			opt_str += '--parallel ' + ('TRUE' if val else 'FALSE') + ' '
 		elif key == 'update_order':
 			opt_str += '--update-order ' + ('TRUE' if val else 'FALSE') + ' '
+		elif key == 'sort_graphs':
+			opt_str += '--sort-graphs ' + ('TRUE' if val else 'FALSE') + ' '
 		elif key == 'refine':
  			opt_str += '--refine ' + ('TRUE' if val else 'FALSE') + ' '
 		elif key == 'time_limit':
diff --git a/gklearn/ged/util/util.py b/gklearn/ged/util/util.py
index a18b0cb..7032345 100644
--- a/gklearn/ged/util/util.py
+++ b/gklearn/ged/util/util.py
@@ -46,7 +46,7 @@ def compute_ged(g1, g2, options):
 	return dis, pi_forward, pi_backward
 
 
-def compute_geds(graphs, options={}, parallel=False):
+def compute_geds(graphs, options={}, sort=True, parallel=False, verbose=True):
 	# initialize ged env.
 	ged_env = gedlibpy.GEDEnv()
 	ged_env.set_edit_cost(options['edit_cost'], edit_cost_constant=options['edit_cost_constants'])
@@ -54,6 +54,8 @@ def compute_geds(graphs, options={}, parallel=False):
 		ged_env.add_nx_graph(g, '')
 	listID = ged_env.get_all_graph_ids()	
 	ged_env.init()
+	if parallel:
+		options['threads'] = 1
 	ged_env.set_method(options['method'], ged_options_to_string(options))
 	ged_env.init_method()
 
@@ -77,10 +79,13 @@ def compute_geds(graphs, options={}, parallel=False):
 			G_graphs = graphs_toshare
 			G_ged_env = ged_env_toshare
 			G_listID = listID_toshare
-		do_partial = partial(_wrapper_compute_ged_parallel, neo_options)
+		do_partial = partial(_wrapper_compute_ged_parallel, neo_options, sort)
 		pool = Pool(processes=n_jobs, initializer=init_worker, initargs=(graphs, ged_env, listID))
-		iterator = tqdm(pool.imap_unordered(do_partial, itr, chunksize),
+		if verbose:
+			iterator = tqdm(pool.imap_unordered(do_partial, itr, chunksize),
 						desc='computing GEDs', file=sys.stdout)
+		else:
+			iterator = pool.imap_unordered(do_partial, itr, chunksize)
 #		iterator = pool.imap_unordered(do_partial, itr, chunksize)
 		for i, j, dis, n_eo_tmp in iterator:
 			idx_itr = int(len(graphs) * i + j - (i + 1) * (i + 2) / 2)
@@ -96,28 +101,38 @@ def compute_geds(graphs, options={}, parallel=False):
 	else:
 		ged_vec = []
 		n_edit_operations = []
-		for i in tqdm(range(len(graphs)), desc='computing GEDs', file=sys.stdout):
+		if verbose:
+			iterator = tqdm(range(len(graphs)), desc='computing GEDs', file=sys.stdout)
+		else:
+			iterator = range(len(graphs))
+		for i in iterator:
 #		for i in range(len(graphs)):
 			for j in range(i + 1, len(graphs)):
-				dis, pi_forward, pi_backward = _compute_ged(ged_env, listID[i], listID[j], graphs[i], graphs[j])
+				if nx.number_of_nodes(graphs[i]) <= nx.number_of_nodes(graphs[j]) or not sort:
+					dis, pi_forward, pi_backward = _compute_ged(ged_env, listID[i], listID[j], graphs[i], graphs[j])
+				else:
+					dis, pi_backward, pi_forward = _compute_ged(ged_env, listID[j], listID[i], graphs[j], graphs[i])
 				ged_vec.append(dis)
 				ged_mat[i][j] = dis
 				ged_mat[j][i] = dis
-				n_eo_tmp = get_nb_edit_operations(graphs[i], graphs[j], pi_forward, pi_backward, **neo_options)
+				n_eo_tmp = get_nb_edit_operations(graphs[i], graphs[j], pi_forward, pi_backward, 	**neo_options)
 				n_edit_operations.append(n_eo_tmp)
-					
+
 	return ged_vec, ged_mat, n_edit_operations
 
 
-def _wrapper_compute_ged_parallel(options, itr):
+def _wrapper_compute_ged_parallel(options, sort, itr):
 	i = itr[0]
 	j = itr[1]
-	dis, n_eo_tmp = _compute_ged_parallel(G_ged_env, G_listID[i], G_listID[j], G_graphs[i], G_graphs[j], options)
+	dis, n_eo_tmp = _compute_ged_parallel(G_ged_env, G_listID[i], G_listID[j], G_graphs[i], G_graphs[j], options, sort)
 	return i, j, dis, n_eo_tmp
 
 
-def _compute_ged_parallel(env, gid1, gid2, g1, g2, options):
-	dis, pi_forward, pi_backward = _compute_ged(env, gid1, gid2, g1, g2)
+def _compute_ged_parallel(env, gid1, gid2, g1, g2, options, sort):
+	if nx.number_of_nodes(g1) <= nx.number_of_nodes(g2) or not sort:
+		dis, pi_forward, pi_backward = _compute_ged(env, gid1, gid2, g1, g2)
+	else:
+		dis, pi_backward, pi_forward = _compute_ged(env, gid2, gid1, g2, g1)
 	n_eo_tmp = get_nb_edit_operations(g1, g2, pi_forward, pi_backward, **options) # [0,0,0,0,0,0]
 	return dis, n_eo_tmp
 
diff --git a/gklearn/gedlib/gedlibpy.cpp b/gklearn/gedlib/gedlibpy.cpp
index 58aa1fd..18e7cd8 100644
--- a/gklearn/gedlib/gedlibpy.cpp
+++ b/gklearn/gedlib/gedlibpy.cpp
@@ -1173,9 +1173,9 @@ typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;
  */
 typedef npy_cdouble __pyx_t_5numpy_complex_t;
 
-/* "gedlibpy.pyx":180
- * 
+/* "gedlibpy.pyx":182
  * 
+ * # @cython.auto_pickle(True)
  * cdef class GEDEnv:             # <<<<<<<<<<<<<<
  * 	"""Cython wrapper class for C++ class PyGEDEnv
  * 	"""
@@ -2155,6 +2155,8 @@ static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, cha
 static PyTypeObject *__pyx_ptype_7cpython_5array_array = 0;
 static CYTHON_INLINE int __pyx_f_7cpython_5array_extend_buffer(arrayobject *, char *, Py_ssize_t); /*proto*/
 
+/* Module declarations from 'cython' */
+
 /* Module declarations from 'gedlibpy' */
 static PyTypeObject *__pyx_ptype_8gedlibpy_GEDEnv = 0;
 static CYTHON_INLINE PyObject *__pyx_convert_PyObject_string_to_py_std__in_string(std::string const &); /*proto*/
@@ -2685,7 +2687,7 @@ static PyObject *__pyx_codeobj__37;
 static PyObject *__pyx_codeobj__39;
 /* Late includes */
 
-/* "gedlibpy.pyx":128
+/* "gedlibpy.pyx":129
  * 
  * 
  * def get_edit_cost_options() :             # <<<<<<<<<<<<<<
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  * 		print("Loading graphs in progress...")
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  * 		print("Loading graphs in progress...")             # <<<<<<<<<<<<<<
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  * 		print("Loading graphs in progress...")
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  * 		print("Loading graphs in progress...")
  * 		for graph in dataset :
  * 			self.add_nx_graph(graph, classes)             # <<<<<<<<<<<<<<
  * 		listID = self.graph_ids()
  * 		print("Graphs loaded ! ")
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@@ -10119,13 +10121,13 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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  * 		for graph in dataset :
  * 			self.add_nx_graph(graph, classes)
  * 		listID = self.graph_ids()             # <<<<<<<<<<<<<<
  * 		print("Graphs loaded ! ")
  * 		print("Number of graphs = " + str(listID[1]))
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-  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_self), __pyx_n_s_graph_ids); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 980, __pyx_L1_error)
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-  /* "gedlibpy.pyx":984
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  * 		print("Number of graphs = " + str(listID[1]))
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  * 		self.set_edit_cost(edit_cost)             # <<<<<<<<<<<<<<
  * 		print("Initialization in progress...")
  * 		self.init(init_option)
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@@ -10232,30 +10234,30 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-  /* "gedlibpy.pyx":985
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  * 		print("Initialization in progress...")             # <<<<<<<<<<<<<<
  * 		self.init(init_option)
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-  /* "gedlibpy.pyx":986
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  * 		self.set_edit_cost(edit_cost)
  * 		print("Initialization in progress...")
  * 		self.init(init_option)             # <<<<<<<<<<<<<<
  * 		print("Initialization terminated !")
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-  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_self), __pyx_n_s_init); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 986, __pyx_L1_error)
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@@ -10269,30 +10271,30 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-  /* "gedlibpy.pyx":987
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  * 		print("Initialization in progress...")
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-  __pyx_t_2 = PyList_New(0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 992, __pyx_L1_error)
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-  __pyx_t_1 = PyList_New(0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 993, __pyx_L1_error)
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-      /* "gedlibpy.pyx":999
+      /* "gedlibpy.pyx":1007
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@@ -10631,7 +10633,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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@@ -10639,13 +10641,13 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-      /* "gedlibpy.pyx":1000
+      /* "gedlibpy.pyx":1008
  * 				self.run_method(g, h)
  * 				resDistance[g][h] = self.get_upper_bound(g, h)
  * 				resMapping[g][h] = self.get_node_map(g, h)             # <<<<<<<<<<<<<<
  * 
  * 		print("Finish ! The return contains edit distances and NodeMap but you can check the result with graphs'ID until you restart the environment")
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-        __pyx_t_12 = PyTuple_New(2+__pyx_t_8); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1000, __pyx_L1_error)
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@@ -10716,18 +10718,18 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-      /* "gedlibpy.pyx":996
+      /* "gedlibpy.pyx":1004
  * 		for g in range(listID[0], listID[1]) :
  * 			print("Computation between graph " + str(g) + " with all the others including himself.")
  * 			for h in range(listID[0], listID[1]) :             # <<<<<<<<<<<<<<
@@ -10737,7 +10739,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-    /* "gedlibpy.pyx":994
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  * 		resDistance = [[]]
  * 		resMapping = [[]]
  * 		for g in range(listID[0], listID[1]) :             # <<<<<<<<<<<<<<
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-  /* "gedlibpy.pyx":1002
+  /* "gedlibpy.pyx":1010
  * 				resMapping[g][h] = self.get_node_map(g, h)
  * 
  * 		print("Finish ! The return contains edit distances and NodeMap but you can check the result with graphs'ID until you restart the environment")             # <<<<<<<<<<<<<<
  * 		return resDistance, resMapping
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-  /* "gedlibpy.pyx":1003
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  * 
  * 		print("Finish ! The return contains edit distances and NodeMap but you can check the result with graphs'ID until you restart the environment")
  * 		return resDistance, resMapping             # <<<<<<<<<<<<<<
@@ -10766,7 +10768,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
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-  __pyx_t_9 = PyTuple_New(2); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 1003, __pyx_L1_error)
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@@ -10778,7 +10780,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
   __pyx_t_9 = 0;
   goto __pyx_L0;
 
-  /* "gedlibpy.pyx":950
+  /* "gedlibpy.pyx":958
  * 
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@@ -10808,7 +10810,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_90compute_edit_distance_on_nx_graphs
   return __pyx_r;
 }
 
-/* "gedlibpy.pyx":1006
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@@ -10862,19 +10864,19 @@ static PyObject *__pyx_pw_8gedlibpy_6GEDEnv_93compute_edit_distance_on_GXl_graph
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  * 		print("Loading graphs in progress...")
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@@ -11011,25 +11013,25 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_92compute_edit_distance_on_GXl_graph
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  * 		print("Loading graphs in progress...")             # <<<<<<<<<<<<<<
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  * 		print("Loading graphs in progress...")
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@@ -11046,7 +11048,7 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_92compute_edit_distance_on_GXl_graph
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@@ -11054,13 +11056,13 @@ static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_92compute_edit_distance_on_GXl_graph
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  * 		self.load_GXL_graphs(path_folder, path_XML)
  * 		listID = self.graph_ids()             # <<<<<<<<<<<<<<
  * 		print("Graphs loaded ! ")
  * 		print("Number of graphs = " + str(listID[1]))
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-  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_self), __pyx_n_s_graph_ids); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1035, __pyx_L1_error)
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  * 		print("Graphs loaded ! ")
  * 		print("Number of graphs = " + str(listID[1]))             # <<<<<<<<<<<<<<
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-  /* "gedlibpy.pyx":1039
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  * 		print("Number of graphs = " + str(listID[1]))
  * 
  * 		self.set_edit_cost(edit_cost)             # <<<<<<<<<<<<<<
  * 		print("Initialization in progress...")
  * 		self.init(init_option)
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-  /* "gedlibpy.pyx":1040
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  * 		self.set_edit_cost(edit_cost)
  * 		print("Initialization in progress...")             # <<<<<<<<<<<<<<
  * 		self.init(init_option)
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-  /* "gedlibpy.pyx":1041
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  * 		self.set_edit_cost(edit_cost)
  * 		print("Initialization in progress...")
  * 		self.init(init_option)             # <<<<<<<<<<<<<<
  * 		print("Initialization terminated !")
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+      /* "gedlibpy.pyx":1058
  * 		for g in range(listID[0], listID[1]) :
  * 			print("Computation between graph " + str(g) + " with all the others including himself.")
  * 			for h in range(listID[0], listID[1]) :             # <<<<<<<<<<<<<<
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-  /* "gedlibpy.pyx":1057
+  /* "gedlibpy.pyx":1065
  * 		#return res
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  * 		print ("Finish ! You can check the result with each ID of graphs ! There are in the return")             # <<<<<<<<<<<<<<
  * 		print ("Please don't restart the environment or recall this function, you will lose your results !")
  * 		return listID
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+  /* "gedlibpy.pyx":1066
  * 
  * 		print ("Finish ! You can check the result with each ID of graphs ! There are in the return")
  * 		print ("Please don't restart the environment or recall this function, you will lose your results !")             # <<<<<<<<<<<<<<
  * 		return listID
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+  /* "gedlibpy.pyx":1067
  * 		print ("Finish ! You can check the result with each ID of graphs ! There are in the return")
  * 		print ("Please don't restart the environment or recall this function, you will lose your results !")
  * 		return listID             # <<<<<<<<<<<<<<
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   __pyx_r = __pyx_v_listID;
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  * 
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  * 		nb_nodes = self.get_graph_num_nodes(graph_id)
  * 		original_node_ids = self.get_original_node_ids(graph_id)
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  * 		for node_id in range(0, nb_nodes):
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-  /* "gedlibpy.pyx":977
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  * 			self.restart_env()
  * 
  * 		print("Loading graphs in progress...")             # <<<<<<<<<<<<<<
  * 		for graph in dataset :
  * 			self.add_nx_graph(graph, classes)
  */
-  __pyx_tuple__4 = PyTuple_Pack(1, __pyx_kp_u_Loading_graphs_in_progress); if (unlikely(!__pyx_tuple__4)) __PYX_ERR(0, 977, __pyx_L1_error)
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-  /* "gedlibpy.pyx":981
+  /* "gedlibpy.pyx":989
  * 			self.add_nx_graph(graph, classes)
  * 		listID = self.graph_ids()
  * 		print("Graphs loaded ! ")             # <<<<<<<<<<<<<<
  * 		print("Number of graphs = " + str(listID[1]))
  * 
  */
-  __pyx_tuple__5 = PyTuple_Pack(1, __pyx_kp_u_Graphs_loaded); if (unlikely(!__pyx_tuple__5)) __PYX_ERR(0, 981, __pyx_L1_error)
+  __pyx_tuple__5 = PyTuple_Pack(1, __pyx_kp_u_Graphs_loaded); if (unlikely(!__pyx_tuple__5)) __PYX_ERR(0, 989, __pyx_L1_error)
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   __Pyx_GIVEREF(__pyx_tuple__5);
 
-  /* "gedlibpy.pyx":985
+  /* "gedlibpy.pyx":993
  * 
  * 		self.set_edit_cost(edit_cost)
  * 		print("Initialization in progress...")             # <<<<<<<<<<<<<<
  * 		self.init(init_option)
  * 		print("Initialization terminated !")
  */
-  __pyx_tuple__6 = PyTuple_Pack(1, __pyx_kp_u_Initialization_in_progress); if (unlikely(!__pyx_tuple__6)) __PYX_ERR(0, 985, __pyx_L1_error)
+  __pyx_tuple__6 = PyTuple_Pack(1, __pyx_kp_u_Initialization_in_progress); if (unlikely(!__pyx_tuple__6)) __PYX_ERR(0, 993, __pyx_L1_error)
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   __Pyx_GIVEREF(__pyx_tuple__6);
 
-  /* "gedlibpy.pyx":987
+  /* "gedlibpy.pyx":995
  * 		print("Initialization in progress...")
  * 		self.init(init_option)
  * 		print("Initialization terminated !")             # <<<<<<<<<<<<<<
  * 
  * 		self.set_method(method, options)
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-  __pyx_tuple__7 = PyTuple_Pack(1, __pyx_kp_u_Initialization_terminated); if (unlikely(!__pyx_tuple__7)) __PYX_ERR(0, 987, __pyx_L1_error)
+  __pyx_tuple__7 = PyTuple_Pack(1, __pyx_kp_u_Initialization_terminated); if (unlikely(!__pyx_tuple__7)) __PYX_ERR(0, 995, __pyx_L1_error)
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   __Pyx_GIVEREF(__pyx_tuple__7);
 
-  /* "gedlibpy.pyx":1002
+  /* "gedlibpy.pyx":1010
  * 				resMapping[g][h] = self.get_node_map(g, h)
  * 
  * 		print("Finish ! The return contains edit distances and NodeMap but you can check the result with graphs'ID until you restart the environment")             # <<<<<<<<<<<<<<
  * 		return resDistance, resMapping
  * 
  */
-  __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_u_Finish_The_return_contains_edit); if (unlikely(!__pyx_tuple__8)) __PYX_ERR(0, 1002, __pyx_L1_error)
+  __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_u_Finish_The_return_contains_edit); if (unlikely(!__pyx_tuple__8)) __PYX_ERR(0, 1010, __pyx_L1_error)
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   __Pyx_GIVEREF(__pyx_tuple__8);
 
-  /* "gedlibpy.pyx":1057
+  /* "gedlibpy.pyx":1065
  * 		#return res
  * 
  * 		print ("Finish ! You can check the result with each ID of graphs ! There are in the return")             # <<<<<<<<<<<<<<
  * 		print ("Please don't restart the environment or recall this function, you will lose your results !")
  * 		return listID
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-  __pyx_tuple__9 = PyTuple_Pack(1, __pyx_kp_u_Finish_You_can_check_the_result); if (unlikely(!__pyx_tuple__9)) __PYX_ERR(0, 1057, __pyx_L1_error)
+  __pyx_tuple__9 = PyTuple_Pack(1, __pyx_kp_u_Finish_You_can_check_the_result); if (unlikely(!__pyx_tuple__9)) __PYX_ERR(0, 1065, __pyx_L1_error)
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   __Pyx_GIVEREF(__pyx_tuple__9);
 
-  /* "gedlibpy.pyx":1058
+  /* "gedlibpy.pyx":1066
  * 
  * 		print ("Finish ! You can check the result with each ID of graphs ! There are in the return")
  * 		print ("Please don't restart the environment or recall this function, you will lose your results !")             # <<<<<<<<<<<<<<
  * 		return listID
  * 
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-  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_u_Please_don_t_restart_the_environ); if (unlikely(!__pyx_tuple__10)) __PYX_ERR(0, 1058, __pyx_L1_error)
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@@ -21339,122 +21341,122 @@ static CYTHON_SMALL_CODE int __Pyx_InitCachedConstants(void) {
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   __Pyx_GIVEREF(__pyx_tuple__19);
 
-  /* "gedlibpy.pyx":128
+  /* "gedlibpy.pyx":129
  * 
  * 
  * def get_edit_cost_options() :             # <<<<<<<<<<<<<<
  * 	"""
  * 		Searchs the differents edit cost functions and returns the result.
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-  __pyx_tuple__21 = PyTuple_Pack(1, __pyx_n_s_option); if (unlikely(!__pyx_tuple__21)) __PYX_ERR(0, 128, __pyx_L1_error)
+  __pyx_tuple__21 = PyTuple_Pack(1, __pyx_n_s_option); if (unlikely(!__pyx_tuple__21)) __PYX_ERR(0, 129, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_tuple__21);
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-  /* "gedlibpy.pyx":142
+  /* "gedlibpy.pyx":143
  * 
  * 
  * def get_method_options() :             # <<<<<<<<<<<<<<
  * 	"""
  * 		Searchs the differents method for edit distance computation between graphs and returns the result.
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-  __pyx_tuple__23 = PyTuple_Pack(1, __pyx_n_s_option); if (unlikely(!__pyx_tuple__23)) __PYX_ERR(0, 142, __pyx_L1_error)
+  __pyx_tuple__23 = PyTuple_Pack(1, __pyx_n_s_option); if (unlikely(!__pyx_tuple__23)) __PYX_ERR(0, 143, __pyx_L1_error)
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-  /* "gedlibpy.pyx":155
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  * 
  * 
  * def get_init_options() :             # <<<<<<<<<<<<<<
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  * 		Searchs the differents initialization parameters for the environment computation for graphs and returns the result.
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-  __pyx_tuple__25 = PyTuple_Pack(1, __pyx_n_s_option); if (unlikely(!__pyx_tuple__25)) __PYX_ERR(0, 155, __pyx_L1_error)
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  * def encode_your_map(map_u):             # <<<<<<<<<<<<<<
  * 	"""
  * 		Encodes Python unicode strings in dictionnary `map` to utf-8 byte strings for C++ functions.
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  * 
  * 
  * def decode_your_map(map_b):             # <<<<<<<<<<<<<<
  * 	"""
  * 		Decodes utf-8 byte strings in `map` from C++ functions to Python unicode strings.
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   /* "gedlibpy.pyx":1
diff --git a/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so b/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so
index 94b9401..9d24796 100644
Binary files a/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so and b/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so differ
diff --git a/gklearn/gedlib/gedlibpy.pyx b/gklearn/gedlib/gedlibpy.pyx
index 54f24b0..7fb7e84 100644
--- a/gklearn/gedlib/gedlibpy.pyx
+++ b/gklearn/gedlib/gedlibpy.pyx
@@ -112,6 +112,7 @@ cdef extern from "src/GedLibBind.hpp" namespace "pyged":
 ##CYTHON WRAPPER INTERFACES##
 #############################
 
+# import cython
 import numpy as np
 import networkx as nx
 from gklearn.ged.env import NodeMap
@@ -177,14 +178,16 @@ def get_dummy_node() :
 	return getDummyNode()
 	
 
+# @cython.auto_pickle(True)
 cdef class GEDEnv:
 	"""Cython wrapper class for C++ class PyGEDEnv
 	"""
-	# cdef PyGEDEnv c_env  # Hold a C++ instance which we're wrapping
+# 	cdef PyGEDEnv c_env  # Hold a C++ instance which we're wrapping
 	cdef PyGEDEnv* c_env  # hold a pointer to the C++ instance which we're wrapping
 
 
 	def __cinit__(self):
+# 		self.c_env = PyGEDEnv()
 		self.c_env = new PyGEDEnv()
 		
 	
@@ -192,6 +195,11 @@ cdef class GEDEnv:
 		del self.c_env
 
 
+# 	def __reduce__(self):
+# # 		return GEDEnv, (self.c_env,)
+# 		return GEDEnv, tuple()
+
+
 	def is_initialized(self) :
 		"""
 			Checks and returns if the computation environment is initialized or not.
diff --git a/gklearn/kernels/graph_kernel.py b/gklearn/kernels/graph_kernel.py
index 6f667e1..db4abf8 100644
--- a/gklearn/kernels/graph_kernel.py
+++ b/gklearn/kernels/graph_kernel.py
@@ -67,6 +67,9 @@ class GraphKernel(object):
 			
 			
 	def normalize_gm(self, gram_matrix):
+		import warnings
+		warnings.warn('gklearn.kernels.graph_kernel.normalize_gm will be deprecated, use gklearn.utils.normalize_gram_matrix instead', DeprecationWarning)
+
 		diag = gram_matrix.diagonal().copy()
 		for i in range(len(gram_matrix)):
 			for j in range(i, len(gram_matrix)):
diff --git a/gklearn/preimage/__init__.py b/gklearn/preimage/__init__.py
index f04b5cc..21e688e 100644
--- a/gklearn/preimage/__init__.py
+++ b/gklearn/preimage/__init__.py
@@ -12,3 +12,4 @@ __date__ = "March 2020"
 
 from gklearn.preimage.preimage_generator import PreimageGenerator
 from gklearn.preimage.median_preimage_generator import MedianPreimageGenerator
+from gklearn.preimage.kernel_knn_cv import kernel_knn_cv
diff --git a/gklearn/preimage/experiments/tools/analyze_results_of_random_edit_costs.py b/gklearn/preimage/experiments/tools/analyze_results_of_random_edit_costs.py
new file mode 100644
index 0000000..bbde39e
--- /dev/null
+++ b/gklearn/preimage/experiments/tools/analyze_results_of_random_edit_costs.py
@@ -0,0 +1,91 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Apr 14 16:57:18 2020
+
+@author: ljia
+"""
+import pandas as pd
+import numpy as np
+import os
+import math
+
+def summarize_results_of_random_edit_costs(data_dir, ds_name, gkernel):
+	sod_sm_list = []
+	sod_gm_list = []
+	dis_k_sm_list = []
+	dis_k_gm_list = []
+	dis_k_min_gi = []
+	time_total_list = []
+	mge_dec_order_list = []
+	mge_inc_order_list = []
+	
+	# get results from .csv.
+	file_name = data_dir + 'results_summary.' + ds_name + '.' + gkernel + '.csv'
+	try:
+		df = pd.read_csv(file_name)
+	except FileNotFoundError:
+		return
+	for index, row in df.iterrows():
+		if row['target'] == 'all' and row['fit method'] == 'random':
+			if not math.isnan(float(row['SOD SM'])):
+				sod_sm_list.append(float(row['SOD SM']))
+			if not math.isnan(float(row['SOD GM'])):
+				sod_gm_list.append(float(row['SOD GM']))
+			if not math.isnan(float(row['dis_k SM'])):
+				dis_k_sm_list.append(float(row['dis_k SM']))
+			if not math.isnan(float(row['dis_k GM'])):
+				dis_k_gm_list.append(float(row['dis_k GM']))
+			if not math.isnan(float(row['min dis_k gi'])):
+				dis_k_min_gi.append(float(row['min dis_k gi']))
+			if not math.isnan(float(row['time total'])):
+				time_total_list.append(float(row['time total']))
+			if 'mge num decrease order' in row:
+				mge_dec_order_list.append(int(row['mge num decrease order']))
+			if 'mge num increase order' in row:
+				mge_inc_order_list.append(int(row['mge num increase order']))
+	# return if no results.
+	if len(sod_sm_list) == 0:
+		return
+	
+	# construct output results.
+	op = {}
+	op['measure'] = ['max', 'min', 'mean']
+	op['SOD SM'] = [np.max(sod_sm_list), np.min(sod_sm_list), np.mean(sod_sm_list)]
+	op['SOD GM'] = [np.max(sod_gm_list), np.min(sod_gm_list), np.mean(sod_gm_list)]
+	op['dis_k SM'] = [np.max(dis_k_sm_list), np.min(dis_k_sm_list), np.mean(dis_k_sm_list)]
+	op['dis_k GM'] = [np.max(dis_k_gm_list), np.min(dis_k_gm_list), np.mean(dis_k_gm_list)]
+	op['min dis_k gi'] = [np.max(dis_k_min_gi), np.min(dis_k_min_gi), np.mean(dis_k_min_gi)]
+	op['time total'] = [np.max(time_total_list), np.min(time_total_list), np.mean(time_total_list)]
+	if len(mge_dec_order_list) > 0:
+		op['mge num decrease order'] = [np.max(mge_dec_order_list), np.min(mge_dec_order_list), np.mean(mge_dec_order_list)]
+	if len(mge_inc_order_list) > 0:
+		op['mge num increase order'] = [np.max(mge_inc_order_list), np.min(mge_inc_order_list), np.mean(mge_inc_order_list)]
+	df = pd.DataFrame(data=op)
+	
+	# write results to .csv
+	df.to_csv(data_dir + 'summary_for_random_edit_costs.csv', index=False, header=True)
+	
+	
+def compute_for_all_experiments(data_dir):
+	dir_list = [i for i in os.listdir(data_dir) if os.path.isdir(data_dir + i)]
+	for dir_name in dir_list:
+		sp_tmp = dir_name.split('.')
+		ds_name = sp_tmp[0].strip('[error]')
+		gkernel = sp_tmp[1]
+		summarize_results_of_random_edit_costs(data_dir + dir_name + '/',
+										 ds_name, gkernel)
+		if os.path.exists(data_dir + dir_name + '/update_order/'):
+			summarize_results_of_random_edit_costs(data_dir + dir_name + '/update_order/',
+										 ds_name, gkernel)
+
+
+if __name__ == '__main__':
+# 	data_dir = '../results/xp_median_preimage.update_order/'
+	root_dir_tnz = '../../results/CRIANN/xp_median_preimage.init10/'
+	root_dir_ntnz = '../../results/CRIANN/xp_median_preimage.init10.no_triangle_rule/'
+	root_dir_tz = '../../results/CRIANN/xp_median_preimage.init10.triangle_rule.allow_zeros/'
+	root_dir_ntz = '../../results/CRIANN/xp_median_preimage.init10.no_triangle_rule.allow_zeros/'
+	data_dirs = [root_dir_tnz, root_dir_ntnz, root_dir_tz, root_dir_ntz]
+	for data_dir in data_dirs:
+		compute_for_all_experiments(data_dir)
\ No newline at end of file
diff --git a/gklearn/preimage/experiments/tools/preimage_results_to_latex_tables.py b/gklearn/preimage/experiments/tools/preimage_results_to_latex_tables.py
new file mode 100644
index 0000000..301f87f
--- /dev/null
+++ b/gklearn/preimage/experiments/tools/preimage_results_to_latex_tables.py
@@ -0,0 +1,228 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Apr 30 10:16:33 2020
+
+@author: ljia
+"""
+import pandas as pd
+import numpy as np
+import os
+
+
+DS_SYMB = ['MUTAG', 'Monoterpenoides', 'MAO_symb']
+DS_NON_SYMB = ['Letter-high', 'Letter-med', 'Letter-low', 'COIL-RAG', 'PAH']
+DS_UNLABELED = ['PAH_unlabeled']
+
+
+def rounder(x, decimals):
+	x_strs = str(x).split('.')
+	if len(x_strs) == 2:
+		before = x_strs[0]
+		after = x_strs[1]
+		if len(after) > decimals:
+			if int(after[decimals]) >= 5:
+				after0s = ''
+				for c in after:
+					if c == '0':
+						after0s += '0'
+					elif c != '0':
+						break
+				after = after0s + str(int(after[0:decimals]) + 1)[-decimals:]
+			else:
+				after = after[0:decimals]
+		elif len(after) < decimals:
+			after += '0' * (decimals - len(after))
+		return before + '.' + after
+
+	elif len(x_strs) == 1:
+		return x_strs[0]
+	
+
+def replace_nth(string, sub, wanted, n):
+	import re
+	where = [m.start() for m in re.finditer(sub, string)][n-1]
+	before = string[:where]
+	after = string[where:]
+	after = after.replace(sub, wanted, 1)
+	newString = before + after
+	return newString
+
+
+def df_to_latex_table(df):
+	ltx = df.to_latex(index=True, escape=False, multirow=True)
+	
+	# modify middle lines.
+	ltx = ltx.replace('\\cline{1-9}\n\\cline{2-9}', 	'\\toprule')
+	ltx = ltx.replace('\\cline{2-9}', '\\cmidrule(l){2-9}')
+	
+	# modify first row.
+	i_start = ltx.find('\n\\toprule\n')
+	i_end = ltx.find('\\\\\n\\midrule\n')
+	ltx = ltx.replace(ltx[i_start:i_end+12], '\n\\toprule\nDatasets & Graph Kernels & Algorithms & $d_\\mathcal{F}$ SM & $d_\\mathcal{F}$ SM (UO) & $d_\\mathcal{F}$ GM & $d_\\mathcal{F}$ GM (UO) & Runtime & Runtime (UO) \\\\\n\\midrule\n', 1)
+	
+	# add row numbers.
+	ltx = ltx.replace('lllllllll', 'lllllllll|@{\\makebox[2em][r]{\\textit{\\rownumber\\space}}}', 1)
+	ltx = replace_nth(ltx, '\\\\\n', '\\gdef\\rownumber{\\stepcounter{magicrownumbers}\\arabic{magicrownumbers}} \\\\\n', 1)
+		
+	return ltx
+
+
+def beautify_df(df):
+	df = df.sort_values(by=['Datasets', 'Graph Kernels'])
+	df = df.set_index(['Datasets', 'Graph Kernels', 'Algorithms'])
+# 	index = pd.MultiIndex.from_frame(df[['Datasets', 'Graph Kernels', 'Algorithms']])
+
+	# bold the best results.
+	for ds in df.index.get_level_values('Datasets').unique():
+		for gk in df.loc[ds].index.get_level_values('Graph Kernels').unique():
+			min_val = np.inf
+			min_indices = []
+			min_labels = []
+			for index, row in df.loc[(ds, gk)].iterrows():
+				for label in ['$d_\mathcal{F}$ SM', '$d_\mathcal{F}$ GM', '$d_\mathcal{F}$ GM (UO)']:
+					value = row[label]
+					if value != '-':
+						value = float(value.strip('/same'))
+						if value < min_val:
+							min_val = value
+							min_indices = [index]
+							min_labels = [label]
+						elif value == min_val:
+							min_indices.append(index)
+							min_labels.append(label)
+			for idx, index in enumerate(min_indices):
+				df.loc[(ds, gk, index), min_labels[idx]] = '\\textbf{' + df.loc[(ds, gk, index), min_labels[idx]] + '}'
+	
+	return df
+
+
+def get_results(data_dir, ds_name, gkernel):
+	# get results from .csv.
+	file_name = data_dir + 'results_summary.' + ds_name + '.' + gkernel + '.csv'
+	try:
+		df_summary = pd.read_csv(file_name)
+	except FileNotFoundError:
+		return None
+
+	df_results = pd.DataFrame(index=None, columns=['d_F SM', 'd_F GM', 'runtime'])
+	for index, row in df_summary.iterrows():
+		if row['target'] == 'all' and row['fit method'] == 'k-graphs':
+			df_results.loc['From median set'] = ['-', rounder(row['min dis_k gi'], 3), '-']
+			if_uo = (int(row['mge num decrease order']) > 0 or int(row['mge num increase order']) > 0)
+			df_results.loc['Optimized'] = [rounder(row['dis_k SM'], 3), 
+								  rounder(row['dis_k GM'], 3) if if_uo else (rounder(row['dis_k GM'], 3) + '/same'),
+								  rounder(row['time total'], 2)]
+		if row['target'] == 'all' and row['fit method'] == 'expert':
+			if_uo = (int(row['mge num decrease order']) > 0 or int(row['mge num increase order']) > 0)
+			df_results.loc['IAM: expert costs'] = [rounder(row['dis_k SM'], 3), 
+								  rounder(row['dis_k GM'], 3) if if_uo else (rounder(row['dis_k GM'], 3) + '/same'),
+								  rounder(row['time total'], 2)]
+								  
+	# get results from random summary .csv.
+	random_fini = True
+	file_name = data_dir + 'summary_for_random_edit_costs.csv'
+	try:
+		df_random = pd.read_csv(file_name)
+	except FileNotFoundError:
+		random_fini = False
+
+	if random_fini:								  
+		for index, row in df_random.iterrows():
+			if row['measure'] == 'mean':
+				if_uo = (float(row['mge num decrease order']) > 0 or float(row['mge num increase order']) > 0)
+				df_results.loc['IAM: random costs'] = [rounder(row['dis_k SM'], 3), 
+								  rounder(row['dis_k GM'], 3) if if_uo else (rounder(row['dis_k GM'], 3) + '/same'),
+								  rounder(row['time total'], 2)]
+				
+	# sort index.
+	df_results = df_results.reindex([item for item in ['From median set', 'IAM: random costs', 'IAM: expert costs', 'Optimized'] if item in df_results.index])
+				
+	return df_results
+	
+
+def get_results_of_one_xp(data_dir, ds_name, gkernel):
+	df_results = pd.DataFrame()
+	
+	df_tmp_uo = None
+	if not os.path.isfile(data_dir + 'update_order/error.txt'):
+		df_tmp_uo = get_results(data_dir + 'update_order/', ds_name, gkernel)
+
+	df_tmp = None
+	if not os.path.isfile(data_dir + 'error.txt'):
+		df_tmp = get_results(data_dir, ds_name, gkernel)
+
+	if (df_tmp_uo is not None and not df_tmp_uo.empty) or (df_tmp is not None and not df_tmp.empty):
+		df_results = pd.DataFrame(index=['From median set', 'IAM: random costs', 'IAM: expert costs', 'Optimized'], columns=['$d_\mathcal{F}$ SM', '$d_\mathcal{F}$ SM (UO)', '$d_\mathcal{F}$ GM', '$d_\mathcal{F}$ GM (UO)', 'Runtime', 'Runtime (UO)'])
+		if df_tmp_uo is not None and not df_tmp_uo.empty:
+			for index, row in df_tmp_uo.iterrows():
+				for algo in df_results.index:
+					if index == algo:
+						df_results.at[algo, '$d_\mathcal{F}$ SM (UO)'] = row['d_F SM']
+						df_results.at[algo, '$d_\mathcal{F}$ GM (UO)'] = row['d_F GM']
+						df_results.at[algo, 'Runtime (UO)'] = row['runtime']
+		if df_tmp is not None and not df_tmp.empty:
+			for index, row in df_tmp.iterrows():
+				for algo in df_results.index:
+					if index == algo:
+						df_results.at[algo, '$d_\mathcal{F}$ SM'] = row['d_F SM']
+						df_results.at[algo, '$d_\mathcal{F}$ GM'] = row['d_F GM'].strip('/same')
+						df_results.at[algo, 'Runtime'] = row['runtime']	
+	
+	df_results = df_results.dropna(axis=0, how='all')
+	df_results = df_results.fillna(value='-')
+	df_results = df_results.reset_index().rename(columns={'index': 'Algorithms'})
+		
+	return df_results
+
+
+def get_results_for_all_experiments(root_dir):
+	columns=['Datasets', 'Graph Kernels', 'Algorithms', '$d_\mathcal{F}$ SM', '$d_\mathcal{F}$ SM (UO)', '$d_\mathcal{F}$ GM', '$d_\mathcal{F}$ GM (UO)', 'Runtime', 'Runtime (UO)']
+	df_symb = pd.DataFrame(columns=columns)
+	df_nonsymb = pd.DataFrame(columns=columns)
+	df_unlabeled = pd.DataFrame(columns=columns)
+	
+	dir_list = [i for i in os.listdir(root_dir) if os.path.isdir(root_dir + i)]
+	for dir_name in dir_list:
+		sp_tmp = dir_name.split('.')
+		gkernel = sp_tmp[1]
+		ds_name = sp_tmp[0].strip('[error]')
+		suffix = ''
+		if sp_tmp[-1] == 'unlabeled':
+ 			suffix = '_unlabeled'
+		elif sp_tmp[-1] == 'symb':
+ 			suffix = '_symb'
+			 
+		df_results = get_results_of_one_xp(root_dir + dir_name + '/', ds_name, gkernel)
+		
+		if not df_results.empty:
+			ds_name += suffix
+			if ds_name in DS_SYMB:
+				for index, row in df_results.iterrows():
+					df_symb.loc[len(df_symb)] = [ds_name.replace('_', '\_'), gkernel] + row.tolist()
+			elif ds_name in DS_NON_SYMB:
+				for index, row in df_results.iterrows():
+					df_nonsymb.loc[len(df_nonsymb)] = [ds_name.replace('_', '\_'), gkernel] + row.tolist()
+			elif ds_name in DS_UNLABELED:
+				for index, row in df_results.iterrows():
+					df_unlabeled.loc[len(df_unlabeled)] = [ds_name.replace('_', '\_'), gkernel] + row.tolist()
+			else:
+				raise Exception('dataset' + ds_name + 'is not pre-defined.')
+				
+	# sort.
+	df_symb = beautify_df(df_symb)
+	df_nonsymb = beautify_df(df_nonsymb)
+	df_unlabeled = beautify_df(df_unlabeled)
+	
+	# convert dfs to latex strings.
+	ltx_symb = df_to_latex_table(df_symb)
+	ltx_nonsymb = df_to_latex_table(df_nonsymb)
+	ltx_unlabeled = df_to_latex_table(df_unlabeled)
+	
+	return ltx_symb, ltx_nonsymb, ltx_unlabeled
+
+
+if __name__ == '__main__':
+# 	root_dir = '../results/xp_median_preimage.init20/'
+	root_dir = '../../results/CRIANN/xp_median_preimage.init10/'
+	ltx_symb, ltx_nonsymb, ltx_unlabeled = get_results_for_all_experiments(root_dir)
diff --git a/gklearn/preimage/experiments/xp_1nn_init10_trianglerule.py b/gklearn/preimage/experiments/xp_1nn_init10_trianglerule.py
new file mode 100644
index 0000000..d23e119
--- /dev/null
+++ b/gklearn/preimage/experiments/xp_1nn_init10_trianglerule.py
@@ -0,0 +1,3382 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri May 15 10:50:46 2020
+
+@author: ljia
+"""
+import multiprocessing
+import functools
+import sys
+import os
+import logging
+from gklearn.utils.kernels import deltakernel, gaussiankernel, kernelproduct
+from gklearn.preimage import kernel_knn_cv
+from gklearn.utils import compute_gram_matrices_by_class
+
+
+dir_root = '../results/xp_1nn.init10.triangle_rule/'
+initial_solutions = 10
+triangle_rule = True
+allow_zeros = False
+update_order = False
+test_sizes = [0.9, 0.7] # , 0.5, 0.3, 0.1]
+
+
+def xp_median_preimage_15_1():
+	"""xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'AIDS' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_15_2():
+	"""xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'AIDS' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 1, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_15_3():
+	"""xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'AIDS' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		pkernel = functools.partial(polynomialkernel, d=1, c=1e+2)
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_15_4():
+	"""xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'AIDS' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 10,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_14_1():
+	"""xp 14_1: DD, PathUpToH, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'DD' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 2, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+	
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+	# 	# compute gram matrices for each class a priori.
+	# 	print('Compute gram matrices for each class a priori.')
+	# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=save_results, dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_13_1():
+	"""xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_13_2():
+	"""xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '') # 
+		irrelevant_labels = None # 
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']: # 
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_12_1():
+	"""xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 0, 1, 1, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_2():
+	"""xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 1, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+
+def xp_median_preimage_12_3():
+	"""xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+	"""
+	from gklearn.utils.kernels import gaussiankernel
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		pkernel = functools.partial(gaussiankernel, gamma=None) # @todo
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_4():
+	"""xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 14,
+						  'base_kernel': 'subtree',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+	# 	# compute gram matrices for each class a priori.
+	# 	print('Compute gram matrices for each class a priori.')
+	# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_5():
+	"""xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'PAH' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 0, 1, 1, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' # 
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']: # 
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_9_1():
+	"""xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MAO' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_2():
+	"""xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MAO' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 9, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_3():
+	"""xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'MAO' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		pkernel = functools.partial(polynomialkernel, d=4, c=1e+7)
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_4():
+	"""xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MAO' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 6,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_8_1():
+	"""xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_2():
+	"""xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 7, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_3():
+	"""xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		pkernel = functools.partial(polynomialkernel, d=2, c=1e+5)
+		kernel_options = {'name': 'Treelet',
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_4():
+	"""xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 4,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_7_1():
+	"""xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_2():
+	"""xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 2, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_7_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_3():
+	"""xp 7_3: MUTAG, Treelet, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'MUTAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		pkernel = functools.partial(polynomialkernel, d=3, c=1e+8)
+		kernel_options = {'name': 'Treelet',
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_4():
+	"""xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 1,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_6_1():
+	"""xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'COIL-RAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_6_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_6_2():
+	"""xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'COIL-RAG' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_6_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+
+def xp_median_preimage_5_1():
+	"""xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'FRANKENSTEIN' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_4_1():
+	"""xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'COLORS-3' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_3_2():
+	"""xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Fingerprint' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.01, 0.125, 0.125], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'edge_attrs': ['orient', 'angle']} #
+		edge_required = True #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_3_1():
+	"""xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Fingerprint' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.01, 0.125, 0.125], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'edge_attrs': ['orient', 'angle']} #
+		edge_required = False #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_2_1():
+	"""xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'COIL-DEL' #
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.node_attrs/'
+		irrelevant_labels = {'edge_labels': ['valence']}
+		edge_required = False
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_1_1():
+	"""xp 1_1: Letter-high, StructuralSP.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-high'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.675, 0.675, 0.75, 0.425, 0.425],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None
+		edge_required = False
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_1_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_1_2():
+	"""xp 1_2: Letter-high, ShortestPath.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-high'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.675, 0.675, 0.75, 0.425, 0.425],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_1_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_10_1():
+	"""xp 10_1: Letter-med, StructuralSP.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-med'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.75, 0.475, 0.475],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None
+		edge_required = False
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_10_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_10_2():
+	"""xp 10_2: Letter-med, ShortestPath.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-med'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.75, 0.475, 0.475],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_10_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+
+def xp_median_preimage_11_1():
+	"""xp 11_1: Letter-low, StructuralSP.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-low'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.075, 0.075, 0.25, 0.075, 0.075],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None
+		edge_required = False
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_11_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_11_2():
+	"""xp 11_2: Letter-low, ShortestPath.
+	"""
+	for test_size in test_sizes:
+		# set parameters.
+		ds_name = 'Letter-low'
+		knn_options = {'n_neighbors': 1,
+					   'n_splits': 30,
+					   'test_size': test_size,
+					   'verbose': True}
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.075, 0.075, 0.25, 0.075, 0.075],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'allow_zeros': allow_zeros,
+					   'triangle_rule': triangle_rule,
+					   'verbose': 1}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 0}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 1,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('knn_options:', knn_options)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for train_examples in ['k-graphs', 'expert', 'random', 'best-dataset', 'trainset']:
+			print('\n-------------------------------------')
+			print('train examples used:', train_examples, '\n')
+			mpg_options['fit_method'] = train_examples
+			try:
+				kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_11_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+if __name__ == "__main__":
+	
+# 	#### xp 1_1: Letter-high, StructuralSP.
+ 	# xp_median_preimage_1_1()
+
+# 	#### xp 1_2: Letter-high, ShortestPath.
+ 	# xp_median_preimage_1_2()
+
+# 	#### xp 10_1: Letter-med, StructuralSP.
+ 	# xp_median_preimage_10_1()
+
+# 	#### xp 10_2: Letter-med, ShortestPath.
+ 	# xp_median_preimage_10_2()
+
+# 	#### xp 11_1: Letter-low, StructuralSP.
+ 	# xp_median_preimage_11_1()
+
+# 	#### xp 11_2: Letter-low, ShortestPath.
+ 	# xp_median_preimage_11_2()
+# 	
+# 	#### xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+# # 	xp_median_preimage_2_1()
+# 	
+# 	#### xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+#  	# xp_median_preimage_3_1()
+
+# 	#### xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+ 	# xp_median_preimage_3_2()
+
+# 	#### xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_4_1()
+# 	
+# 	#### xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_5_1()
+# 	
+# 	#### xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_1()
+
+# 	#### xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_2()
+
+# 	#### xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+ 	# xp_median_preimage_7_1()
+
+# 	#### xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+ 	# xp_median_preimage_7_2()
+
+# 	#### xp 7_3: MUTAG, Treelet, using CONSTANT.
+ 	# xp_median_preimage_7_3()
+
+# 	#### xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+ 	# xp_median_preimage_7_4()
+# 	 
+#     #### xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+ 	# xp_median_preimage_8_1()
+
+# 	#### xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+ 	# xp_median_preimage_8_2()
+
+# 	#### xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+ 	# xp_median_preimage_8_3()
+
+# 	#### xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+ 	# xp_median_preimage_8_4()
+
+# 	#### xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_1()
+
+# 	#### xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_2()
+
+# 	#### xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_3()
+
+# 	#### xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_4()
+
+	#### xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+ 	# xp_median_preimage_12_1()
+
+	#### xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_2()
+
+	#### xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_3()
+
+	#### xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_4()
+
+	#### xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+ 	# xp_median_preimage_12_5()
+
+	#### xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+ 	# xp_median_preimage_13_1()
+
+	#### xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+# 	xp_median_preimage_13_2()
+
+	#### xp 14_1: DD, PathUpToH, using CONSTANT.
+# 	xp_median_preimage_14_1()
+
+# 	#### xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_1()
+
+# 	#### xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_2()
+
+# 	#### xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_3()
+
+# 	#### xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_4()
+
+
+
+
+
+
+# 	#### xp 1_1: Letter-high, StructuralSP.
+ 	xp_median_preimage_1_1()
+
+# 	#### xp 1_2: Letter-high, ShortestPath.
+ 	xp_median_preimage_1_2()
+
+# 	#### xp 10_1: Letter-med, StructuralSP.
+ 	xp_median_preimage_10_1()
+
+# 	#### xp 10_2: Letter-med, ShortestPath.
+ 	xp_median_preimage_10_2()
+
+# 	#### xp 11_1: Letter-low, StructuralSP.
+ 	xp_median_preimage_11_1()
+
+# 	#### xp 11_2: Letter-low, ShortestPath.
+ 	xp_median_preimage_11_2()
+	 
+	#### xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+ 	xp_median_preimage_13_1()
+
+	#### xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+ 	xp_median_preimage_13_2()
+	 
+# 	#### xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+ 	xp_median_preimage_7_2()
+
+# 	#### xp 7_3: MUTAG, Treelet, using CONSTANT.
+ 	xp_median_preimage_7_3()
+
+# 	#### xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+ 	xp_median_preimage_7_4()
+# 	 
+# 	#### xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+ 	xp_median_preimage_7_1()
+
+# 	#### xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_2()
+
+# 	#### xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_3()
+
+# 	#### xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_4()
+	 
+# 	#### xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_1()
+
+	#### xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+ 	xp_median_preimage_12_1()
+
+	#### xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_2()
+
+	#### xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_3()
+
+	#### xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_4()
+
+	#### xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+ 	xp_median_preimage_12_5()
+	 
+# 	#### xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+ 	xp_median_preimage_6_1()
+	 
+# 	#### xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+ 	xp_median_preimage_8_2()
+
+# 	#### xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+ 	xp_median_preimage_8_3()
+
+# 	#### xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+ 	xp_median_preimage_8_4()
+	 
+#     #### xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+ 	xp_median_preimage_8_1()
+	 
+	 # 	#### xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_1()
+
+# 	#### xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_2()
+
+# 	#### xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_3()
+
+# 	#### xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_4()
+# 	
+# 	#### xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+ 	xp_median_preimage_2_1()
+# 	
+# 	#### xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+#  	# xp_median_preimage_3_1()
+
+# 	#### xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+ 	# xp_median_preimage_3_2()
+
+# 	#### xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_4_1()
+# 	
+# 	#### xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_5_1()
+# 	
+# 	#### xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_2()
+
+	#### xp 14_1: DD, PathUpToH, using CONSTANT.
+# 	xp_median_preimage_14_1()
\ No newline at end of file
diff --git a/gklearn/preimage/experiments/xp_remove_best_graph_init10.py b/gklearn/preimage/experiments/xp_remove_best_graph_init10.py
new file mode 100644
index 0000000..8b722ae
--- /dev/null
+++ b/gklearn/preimage/experiments/xp_remove_best_graph_init10.py
@@ -0,0 +1,3085 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jan 14 15:39:29 2020
+
+@author: ljia
+"""
+import multiprocessing
+import functools
+import sys
+import os
+import logging
+from gklearn.utils.kernels import deltakernel, gaussiankernel, kernelproduct
+from gklearn.preimage.remove_best_graph import remove_best_graph
+from gklearn.utils import compute_gram_matrices_by_class
+
+
+dir_root = '../results/xp_remove_best_graph.init10/'
+num_random = 10
+initial_solutions = 10
+
+
+def xp_median_preimage_15_1():
+	"""xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'AIDS' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+
+def xp_median_preimage_15_2():
+	"""xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'AIDS' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 1, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_15_3():
+	"""xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'AIDS' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		pkernel = functools.partial(polynomialkernel, d=1, c=1e+2)
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_15_4():
+	"""xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'AIDS' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 10,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_14_1():
+	"""xp 14_1: DD, PathUpToH, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'DD' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 2, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+	
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+	# 	# compute gram matrices for each class a priori.
+	# 	print('Compute gram matrices for each class a priori.')
+	# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=save_results, dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_13_1():
+	"""xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_13_2():
+	"""xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '') # 
+		irrelevant_labels = None # 
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random: # 
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_12_1():
+	"""xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 0, 1, 1, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_2():
+	"""xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 1, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+
+def xp_median_preimage_12_3():
+	"""xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+	"""
+	from gklearn.utils.kernels import gaussiankernel
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		pkernel = functools.partial(gaussiankernel, gamma=None) # @todo
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_4():
+	"""xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 14,
+						  'base_kernel': 'subtree',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+	# 	# compute gram matrices for each class a priori.
+	# 	print('Compute gram matrices for each class a priori.')
+	# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+		
+		
+def xp_median_preimage_12_5():
+	"""xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'PAH' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 0, 1, 1, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.unlabeled/' + ('update_order/' if update_order else '') # 
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random: # 
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_9_1():
+	"""xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MAO' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_2():
+	"""xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MAO' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 9, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_3():
+	"""xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'MAO' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		pkernel = functools.partial(polynomialkernel, d=4, c=1e+7)
+		kernel_options = {'name': 'Treelet', #
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_9_4():
+	"""xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MAO' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 6,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_8_1():
+	"""xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_2():
+	"""xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 7, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_3():
+	"""xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		pkernel = functools.partial(polynomialkernel, d=2, c=1e+5)
+		kernel_options = {'name': 'Treelet',
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_8_4():
+	"""xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Monoterpenoides' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 4,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_7_1():
+	"""xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_2():
+	"""xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'PathUpToH',
+						  'depth': 2, #
+						  'k_func': 'MinMax', #
+						  'compute_method': 'trie',
+	 					  'parallel': 'imap_unordered', 
+	                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=None)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_7_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_3():
+	"""xp 7_3: MUTAG, Treelet, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		from gklearn.utils.kernels import polynomialkernel
+		# set parameters.
+		ds_name = 'MUTAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		pkernel = functools.partial(polynomialkernel, d=3, c=1e+8)
+		kernel_options = {'name': 'Treelet',
+					      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_7_4():
+	"""xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'MUTAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [4, 4, 2, 1, 1, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100, # 
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		kernel_options = {'name': 'WeisfeilerLehman',
+					      'height': 1,
+						  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'CONSTANT', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_6_1():
+	"""xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'COIL-RAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_6_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_6_2():
+	"""xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'COIL-RAG' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 1], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC', # 
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_6_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+
+def xp_median_preimage_5_1():
+	"""xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'FRANKENSTEIN' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_4_1():
+	"""xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'COLORS-3' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3, 0], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'NON_SYMBOLIC',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = False #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_3_2():
+	"""xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Fingerprint' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.01, 0.125, 0.125], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'edge_attrs': ['orient', 'angle']} #
+		edge_required = True #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_3_1():
+	"""xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Fingerprint' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.01, 0.125, 0.125], #
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'edge_attrs': ['orient', 'angle']} #
+		edge_required = False #
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+def xp_median_preimage_2_1():
+	"""xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'COIL-DEL' #
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [3, 3, 1, 3, 3],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.node_attrs/' + ('update_order/' if update_order else '')
+		irrelevant_labels = {'edge_labels': ['valence']}
+
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+		
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+# 	# compute gram matrices for each class a priori.
+# 	print('Compute gram matrices for each class a priori.')
+# 	compute_gram_matrices_by_class(ds_name, kernel_options, save_results=True, dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels)
+			except Exception as exp:
+				print('An exception occured when running this experiment:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_1_1():
+	"""xp 1_1: Letter-high, StructuralSP.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-high'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.675, 0.675, 0.75, 0.425, 0.425],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_1_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+			
+def xp_median_preimage_1_2():
+	"""xp 1_2: Letter-high, ShortestPath.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-high'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.675, 0.675, 0.75, 0.425, 0.425],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_1_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+
+
+def xp_median_preimage_10_1():
+	"""xp 10_1: Letter-med, StructuralSP.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-med'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.75, 0.475, 0.475],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_10_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_10_2():
+	"""xp 10_2: Letter-med, ShortestPath.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-med'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.525, 0.525, 0.75, 0.475, 0.475],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_10_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+
+def xp_median_preimage_11_1():
+	"""xp 11_1: Letter-low, StructuralSP.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-low'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.075, 0.075, 0.25, 0.075, 0.075],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'StructuralSP',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'edge_kernels': sub_kernels, 
+						  'compute_method': 'naive',
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_11_1:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+				
+			
+def xp_median_preimage_11_2():
+	"""xp 11_2: Letter-low, ShortestPath.
+	"""
+	for update_order in [True, False]:
+		# set parameters.
+		ds_name = 'Letter-low'
+		mpg_options = {'fit_method': 'k-graphs',
+					   'init_ecc': [0.075, 0.075, 0.25, 0.075, 0.075],
+					   'ds_name': ds_name,
+					   'parallel': True, # False
+					   'time_limit_in_sec': 0,
+					   'max_itrs': 100,
+					   'max_itrs_without_update': 3,
+					   'epsilon_residual': 0.01,
+					   'epsilon_ec': 0.1,
+					   'verbose': 2}
+		mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+		sub_kernels = {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel}
+		kernel_options = {'name': 'ShortestPath',
+						  'edge_weight': None,
+						  'node_kernels': sub_kernels,
+						  'parallel': 'imap_unordered', 
+# 						  'parallel': None, 
+						  'n_jobs': multiprocessing.cpu_count(),
+						  'normalize': True,
+						  'verbose': 2}
+		ged_options = {'method': 'IPFP',
+					   'initialization_method': 'RANDOM', # 'NODE'
+					   'initial_solutions': initial_solutions, # 1
+					   'edit_cost': 'LETTER2',
+					   'attr_distance': 'euclidean',
+					   'ratio_runs_from_initial_solutions': 1,
+					   'threads': multiprocessing.cpu_count(),
+					   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+		mge_options = {'init_type': 'MEDOID',
+					   'random_inits': 10,
+					   'time_limit': 0,
+					   'verbose': 2,
+					   'update_order': update_order,
+					   'randomness': 'REAL',
+					   'refine': False}
+		save_results = True
+		dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' + ('update_order/' if update_order else '')
+		irrelevant_labels = None #
+		edge_required = True #
+		
+		if not os.path.exists(dir_save):
+			os.makedirs(dir_save)
+		file_output = open(dir_save + 'output.txt', 'a')
+		sys.stdout = file_output
+
+		# print settings.
+		print('parameters:')
+		print('dataset name:', ds_name)
+		print('mpg_options:', mpg_options)
+		print('kernel_options:', kernel_options)
+		print('ged_options:', ged_options)
+		print('mge_options:', mge_options)
+		print('save_results:', save_results)
+		print('irrelevant_labels:', irrelevant_labels)
+		print()
+		
+		# generate preimages.
+		for fit_method in ['k-graphs', 'expert'] + ['random'] * num_random:
+			print('\n-------------------------------------')
+			print('fit method:', fit_method, '\n')
+			mpg_options['fit_method'] = fit_method
+			try:
+				remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required)
+			except Exception as exp:
+				print('An exception occured when running experiment on xp_median_preimage_11_2:')
+				LOG_FILENAME = dir_save + 'error.txt'
+				logging.basicConfig(filename=LOG_FILENAME, level=logging.DEBUG)
+				logging.exception('')
+				print(repr(exp))
+			
+
+if __name__ == "__main__":
+	
+# 	#### xp 1_1: Letter-high, StructuralSP.
+ 	# xp_median_preimage_1_1()
+
+# 	#### xp 1_2: Letter-high, ShortestPath.
+ 	# xp_median_preimage_1_2()
+
+# 	#### xp 10_1: Letter-med, StructuralSP.
+ 	# xp_median_preimage_10_1()
+
+# 	#### xp 10_2: Letter-med, ShortestPath.
+ 	# xp_median_preimage_10_2()
+
+# 	#### xp 11_1: Letter-low, StructuralSP.
+ 	# xp_median_preimage_11_1()
+
+# 	#### xp 11_2: Letter-low, ShortestPath.
+ 	# xp_median_preimage_11_2()
+# 	
+# 	#### xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+# # 	xp_median_preimage_2_1()
+# 	
+# 	#### xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+#  	# xp_median_preimage_3_1()
+
+# 	#### xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+ 	# xp_median_preimage_3_2()
+
+# 	#### xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_4_1()
+# 	
+# 	#### xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_5_1()
+# 	
+# 	#### xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_1()
+
+# 	#### xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_2()
+
+# 	#### xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+ 	# xp_median_preimage_7_1()
+
+# 	#### xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+ 	# xp_median_preimage_7_2()
+
+# 	#### xp 7_3: MUTAG, Treelet, using CONSTANT.
+ 	# xp_median_preimage_7_3()
+
+# 	#### xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+ 	# xp_median_preimage_7_4()
+# 	 
+#     #### xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+ 	# xp_median_preimage_8_1()
+
+# 	#### xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+ 	# xp_median_preimage_8_2()
+
+# 	#### xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+ 	# xp_median_preimage_8_3()
+
+# 	#### xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+ 	# xp_median_preimage_8_4()
+
+# 	#### xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_1()
+
+# 	#### xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_2()
+
+# 	#### xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_3()
+
+# 	#### xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_9_4()
+
+	#### xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+ 	# xp_median_preimage_12_1()
+
+	#### xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_2()
+
+	#### xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_3()
+
+	#### xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+ 	# xp_median_preimage_12_4()
+
+	#### xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+ 	# xp_median_preimage_12_5()
+
+	#### xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+ 	# xp_median_preimage_13_1()
+
+	#### xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+# 	xp_median_preimage_13_2()
+
+	#### xp 14_1: DD, PathUpToH, using CONSTANT.
+# 	xp_median_preimage_14_1()
+
+# 	#### xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_1()
+
+# 	#### xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_2()
+
+# 	#### xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_3()
+
+# 	#### xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	# xp_median_preimage_15_4()
+
+
+
+
+
+
+
+# 	#### xp 7_2: MUTAG, PathUpToH, using CONSTANT.
+ 	xp_median_preimage_7_2()
+
+# 	#### xp 7_3: MUTAG, Treelet, using CONSTANT.
+ 	xp_median_preimage_7_3()
+
+# 	#### xp 7_4: MUTAG, WeisfeilerLehman, using CONSTANT.
+ 	xp_median_preimage_7_4()
+# 	 
+# 	#### xp 7_1: MUTAG, StructuralSP, using CONSTANT.
+ 	xp_median_preimage_7_1()
+
+# 	#### xp 8_2: Monoterpenoides, PathUpToH, using CONSTANT.
+ 	xp_median_preimage_8_2()
+
+# 	#### xp 8_3: Monoterpenoides, Treelet, using CONSTANT.
+ 	xp_median_preimage_8_3()
+
+# 	#### xp 8_4: Monoterpenoides, WeisfeilerLehman, using CONSTANT.
+ 	xp_median_preimage_8_4()
+	 
+#     #### xp 8_1: Monoterpenoides, StructuralSP, using CONSTANT.
+ 	xp_median_preimage_8_1()
+
+# 	#### xp 9_2: MAO, PathUpToH, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_2()
+
+# 	#### xp 9_3: MAO, Treelet, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_3()
+
+# 	#### xp 9_4: MAO, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_4()
+	 
+# 	#### xp 9_1: MAO, StructuralSP, using CONSTANT, symbolic only.
+ 	xp_median_preimage_9_1()
+
+ 	#### xp 12_1: PAH, StructuralSP, using NON_SYMBOLIC, unlabeled.
+ 	xp_median_preimage_12_1()
+
+ 	#### xp 12_2: PAH, PathUpToH, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_2()
+
+ 	#### xp 12_3: PAH, Treelet, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_3()
+
+ 	#### xp 12_4: PAH, WeisfeilerLehman, using CONSTANT, unlabeled.
+ 	xp_median_preimage_12_4()
+
+ 	#### xp 12_5: PAH, ShortestPath, using NON_SYMBOLIC, unlabeled.
+ 	xp_median_preimage_12_5()
+	 
+# 	#### xp 1_1: Letter-high, StructuralSP.
+ 	xp_median_preimage_1_1()
+
+# 	#### xp 1_2: Letter-high, ShortestPath.
+ 	xp_median_preimage_1_2()
+
+# 	#### xp 10_1: Letter-med, StructuralSP.
+ 	xp_median_preimage_10_1()
+
+# 	#### xp 10_2: Letter-med, ShortestPath.
+ 	xp_median_preimage_10_2()
+
+# 	#### xp 11_1: Letter-low, StructuralSP.
+ 	xp_median_preimage_11_1()
+
+# 	#### xp 11_2: Letter-low, ShortestPath.
+ 	xp_median_preimage_11_2()
+
+ 	#### xp 13_1: PAH, StructuralSP, using NON_SYMBOLIC.
+ 	xp_median_preimage_13_1()
+
+ 	#### xp 13_2: PAH, ShortestPath, using NON_SYMBOLIC.
+ 	xp_median_preimage_13_2()
+	 
+# 	#### xp 6_1: COIL-RAG, StructuralSP, using NON_SYMBOLIC.
+ 	xp_median_preimage_6_1()
+	 
+	 # 	#### xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_1()
+
+# 	#### xp 15_2: AIDS, PathUpToH, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_2()
+
+# 	#### xp 15_3: AIDS, Treelet, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_3()
+
+# 	#### xp 15_4: AIDS, WeisfeilerLehman, using CONSTANT, symbolic only.
+ 	xp_median_preimage_15_4()
+# 	
+# 	#### xp 2_1: COIL-DEL, StructuralSP, using LETTER2, only node attrs.
+ 	xp_median_preimage_2_1()
+# 	
+# 	#### xp 3_1: Fingerprint, StructuralSP, using LETTER2, only node attrs.
+#  	# xp_median_preimage_3_1()
+
+# 	#### xp 3_2: Fingerprint, ShortestPath, using LETTER2, only node attrs.
+ 	# xp_median_preimage_3_2()
+
+# 	#### xp 4_1: COLORS-3, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_4_1()
+# 	
+# 	#### xp 5_1: FRANKENSTEIN, StructuralSP, using NON_SYMBOLIC.
+# # 	xp_median_preimage_5_1()
+# 	
+# 	#### xp 6_2: COIL-RAG, ShortestPath, using NON_SYMBOLIC.
+ 	# xp_median_preimage_6_2()
+
+	#### xp 14_1: DD, PathUpToH, using CONSTANT.
+# 	xp_median_preimage_14_1()
diff --git a/gklearn/preimage/kernel_knn_cv.py b/gklearn/preimage/kernel_knn_cv.py
new file mode 100644
index 0000000..073fa31
--- /dev/null
+++ b/gklearn/preimage/kernel_knn_cv.py
@@ -0,0 +1,418 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue May 12 12:52:15 2020
+
+@author: ljia
+"""
+import numpy as np
+import csv
+import os
+import os.path
+from gklearn.utils import Dataset
+from sklearn.model_selection import ShuffleSplit
+from gklearn.preimage import MedianPreimageGenerator
+from gklearn.utils import normalize_gram_matrix, compute_distance_matrix
+from gklearn.preimage.utils import get_same_item_indices
+from gklearn.utils.knn import knn_classification
+from gklearn.preimage.utils import compute_k_dis
+	
+
+def kernel_knn_cv(ds_name, train_examples, knn_options, mpg_options, kernel_options, ged_options, mge_options, save_results=True, load_gm='auto', dir_save='', irrelevant_labels=None, edge_required=False, cut_range=None):
+	
+	# 1. get dataset.
+	print('1. getting dataset...')
+	dataset_all = Dataset()
+	dataset_all.load_predefined_dataset(ds_name)
+	dataset_all.trim_dataset(edge_required=edge_required)
+	if irrelevant_labels is not None:
+		dataset_all.remove_labels(**irrelevant_labels)
+	if cut_range is not None:
+		dataset_all.cut_graphs(cut_range)
+
+	if save_results:
+		# create result files.
+		print('creating output files...')
+		fn_output_detail, fn_output_summary = __init_output_file_knn(ds_name, kernel_options['name'], mpg_options['fit_method'], dir_save)
+	else:
+		fn_output_detail, fn_output_summary = None, None
+		
+	# 2. compute/load Gram matrix a priori.
+	print('2. computing/loading Gram matrix...')
+	gram_matrix_unnorm, time_precompute_gm = __get_gram_matrix(load_gm, dir_save, ds_name, kernel_options, dataset_all)
+	
+	# 3. perform k-nn CV.
+	print('3. performing k-nn CV...')
+	if train_examples == 'k-graphs' or train_examples == 'expert' or train_examples == 'random':
+		__kernel_knn_cv_median(dataset_all, ds_name, knn_options, mpg_options, kernel_options, mge_options, ged_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary)
+	
+	elif train_examples == 'best-dataset':
+		__kernel_knn_cv_best_ds(dataset_all, ds_name, knn_options, kernel_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary)
+		
+	elif train_examples == 'trainset':
+		__kernel_knn_cv_trainset(dataset_all, ds_name, knn_options, kernel_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary)
+
+	print('\ncomplete.\n')	
+	
+	
+def __kernel_knn_cv_median(dataset_all, ds_name, knn_options, mpg_options, kernel_options, mge_options, ged_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary):
+	Gn = dataset_all.graphs
+	y_all = dataset_all.targets
+	n_neighbors, n_splits, test_size = knn_options['n_neighbors'], knn_options['n_splits'], knn_options['test_size']
+
+	# get shuffles. 
+	train_indices, test_indices, train_nums, y_app = __get_shuffles(y_all, n_splits, test_size)
+	
+	accuracies = [[], [], []]
+	for trial in range(len(train_indices)):
+		print('\ntrial =', trial)
+		
+		train_index = train_indices[trial]
+		test_index = test_indices[trial]
+		G_app = [Gn[i] for i in train_index]
+		G_test = [Gn[i] for i in test_index]
+		y_test = [y_all[i] for i in test_index]
+		gm_unnorm_trial = gram_matrix_unnorm[train_index,:][:,train_index].copy()
+		
+		# compute pre-images for each class.
+		medians = [[], [], []]
+		train_nums_tmp = [0] + train_nums
+		print('\ncomputing pre-image for each class...\n')
+		for i_class in range(len(train_nums_tmp) - 1):
+			print(i_class + 1, 'of', len(train_nums_tmp) - 1, 'classes:')
+			i_start = int(np.sum(train_nums_tmp[0:i_class + 1]))
+			i_end = i_start + train_nums_tmp[i_class + 1]
+			median_set = G_app[i_start:i_end]
+			
+			dataset = dataset_all.copy()
+			dataset.load_graphs([g.copy() for g in median_set], targets=None)
+			mge_options['update_order'] = True
+			mpg_options['gram_matrix_unnorm'] = gm_unnorm_trial[i_start:i_end,i_start:i_end].copy()
+			mpg_options['runtime_precompute_gm'] = 0
+			set_median, gen_median_uo = __generate_median_preimages(dataset, mpg_options, kernel_options, ged_options, mge_options)
+			mge_options['update_order'] = False
+			mpg_options['gram_matrix_unnorm'] = gm_unnorm_trial[i_start:i_end,i_start:i_end].copy()
+			mpg_options['runtime_precompute_gm'] = 0
+			_, gen_median = __generate_median_preimages(dataset, mpg_options, kernel_options, ged_options, mge_options)
+			medians[0].append(set_median)
+			medians[1].append(gen_median)
+			medians[2].append(gen_median_uo)
+			
+		# for each set of medians.
+		print('\nperforming k-nn...')
+		for i_app, G_app in enumerate(medians):
+			# compute dis_mat between medians.
+			dataset = dataset_all.copy()
+			dataset.load_graphs([g.copy() for g in G_app], targets=None)
+			gm_app_unnorm, _ = __compute_gram_matrix_unnorm(dataset, kernel_options.copy())
+			
+			# compute the entire Gram matrix.
+			graph_kernel = __get_graph_kernel(dataset.copy(), kernel_options.copy())
+			kernels_to_medians = []
+			for g in G_app:
+				kernels_to_median, _ = graph_kernel.compute(g, G_test, **kernel_options.copy()) 
+				kernels_to_medians.append(kernels_to_median)
+			kernels_to_medians = np.array(kernels_to_medians)
+			gm_all = np.concatenate((gm_app_unnorm, kernels_to_medians), axis=1)
+			gm_all = np.concatenate((gm_all, np.concatenate((kernels_to_medians.T, gram_matrix_unnorm[test_index,:][:,test_index].copy()), axis=1)), axis=0)
+			
+			gm_all = normalize_gram_matrix(gm_all.copy())
+			dis_mat, _, _, _ = compute_distance_matrix(gm_all)
+			
+			N = len(G_app)
+			
+			d_app = dis_mat[range(N),:][:,range(N)].copy()
+			
+			d_test = np.zeros((N, len(test_index)))
+			for i in range(N):
+				for j in range(len(test_index)):
+					d_test[i, j] = dis_mat[i, j]
+					
+			accuracies[i_app].append(knn_classification(d_app, d_test, y_app, y_test, n_neighbors, verbose=True, text=train_examples))
+			
+		# write result detail.
+		if save_results:
+			f_detail = open(dir_save + fn_output_detail, 'a')
+			print('writing results to files...')
+			for i, median_type in enumerate(['set-median', 'gen median', 'gen median uo']):
+				csv.writer(f_detail).writerow([ds_name, kernel_options['name'], 
+					  train_examples + ': ' + median_type, trial, 
+					  knn_options['n_neighbors'],
+					  len(gm_all), knn_options['test_size'], 
+					  accuracies[i][-1][0], accuracies[i][-1][1]])
+			f_detail.close()
+		
+	results = {}
+	results['ave_perf_train'] = [np.mean([i[0] for i in j], axis=0) for j in accuracies]
+	results['std_perf_train'] = [np.std([i[0] for i in j], axis=0, ddof=1) for j in accuracies]
+	results['ave_perf_test'] = [np.mean([i[1] for i in j], axis=0) for j in accuracies]
+	results['std_perf_test'] = [np.std([i[1] for i in j], axis=0, ddof=1) for j in accuracies]
+
+	# write result summary for each letter. 
+	if save_results:
+		f_summary = open(dir_save + fn_output_summary, 'a')
+		for i, median_type in enumerate(['set-median', 'gen median', 'gen median uo']):
+			csv.writer(f_summary).writerow([ds_name, kernel_options['name'], 
+				  train_examples + ': ' + median_type, 
+				  knn_options['n_neighbors'],
+				  knn_options['test_size'], results['ave_perf_train'][i],
+				  results['ave_perf_test'][i], results['std_perf_train'][i],
+				  results['std_perf_test'][i], time_precompute_gm])
+		f_summary.close()
+		
+		
+def __kernel_knn_cv_best_ds(dataset_all, ds_name, knn_options, kernel_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary):
+	Gn = dataset_all.graphs
+	y_all = dataset_all.targets
+	n_neighbors, n_splits, test_size = knn_options['n_neighbors'], knn_options['n_splits'], knn_options['test_size']
+
+	# get shuffles. 
+	train_indices, test_indices, train_nums, y_app = __get_shuffles(y_all, n_splits, test_size)
+	
+	accuracies = []
+	for trial in range(len(train_indices)):
+		print('\ntrial =', trial)
+		
+		train_index = train_indices[trial]
+		test_index = test_indices[trial]
+		G_app = [Gn[i] for i in train_index]
+		G_test = [Gn[i] for i in test_index]
+		y_test = [y_all[i] for i in test_index]
+		gm_unnorm_trial = gram_matrix_unnorm[train_index,:][:,train_index].copy()
+		
+		# get best graph from trainset according to distance in kernel space for each class.
+		best_graphs = []
+		train_nums_tmp = [0] + train_nums
+		print('\ngetting best graph from trainset for each class...')
+		for i_class in range(len(train_nums_tmp) - 1):
+			print(i_class + 1, 'of', len(train_nums_tmp) - 1, 'classes.')
+			i_start = int(np.sum(train_nums_tmp[0:i_class + 1]))
+			i_end = i_start + train_nums_tmp[i_class + 1]
+			G_class = G_app[i_start:i_end]
+			gm_unnorm_class = gm_unnorm_trial[i_start:i_end,i_start:i_end]
+			gm_class = normalize_gram_matrix(gm_unnorm_class.copy())
+			
+			k_dis_list = []
+			for idx in range(len(G_class)):
+				k_dis_list.append(compute_k_dis(idx, range(0, len(G_class)), [1 / len(G_class)] * len(G_class), gm_class, withterm3=False))
+			idx_k_dis_min = np.argmin(k_dis_list)
+			best_graphs.append(G_class[idx_k_dis_min].copy())
+			
+			
+		# perform k-nn.
+		print('\nperforming k-nn...')
+		# compute dis_mat between medians.
+		dataset = dataset_all.copy()
+		dataset.load_graphs([g.copy() for g in best_graphs], targets=None)
+		gm_app_unnorm, _ = __compute_gram_matrix_unnorm(dataset, kernel_options.copy())
+		
+		# compute the entire Gram matrix.
+		graph_kernel = __get_graph_kernel(dataset.copy(), kernel_options.copy())
+		kernels_to_best_graphs = []
+		for g in best_graphs:
+			kernels_to_best_graph, _ = graph_kernel.compute(g, G_test, **kernel_options.copy()) 
+			kernels_to_best_graphs.append(kernels_to_best_graph)
+		kernels_to_best_graphs = np.array(kernels_to_best_graphs)
+		gm_all = np.concatenate((gm_app_unnorm, kernels_to_best_graphs), axis=1)
+		gm_all = np.concatenate((gm_all, np.concatenate((kernels_to_best_graphs.T, gram_matrix_unnorm[test_index,:][:,test_index].copy()), axis=1)), axis=0)
+		
+		gm_all = normalize_gram_matrix(gm_all.copy())
+		dis_mat, _, _, _ = compute_distance_matrix(gm_all)
+		
+		N = len(best_graphs)
+		
+		d_app = dis_mat[range(N),:][:,range(N)].copy()
+		
+		d_test = np.zeros((N, len(test_index)))
+		for i in range(N):
+			for j in range(len(test_index)):
+				d_test[i, j] = dis_mat[i, j]
+				
+		accuracies.append(knn_classification(d_app, d_test, y_app, y_test, n_neighbors, verbose=True, text=train_examples))
+			
+		# write result detail.
+		if save_results:
+			f_detail = open(dir_save + fn_output_detail, 'a')
+			print('writing results to files...')
+			csv.writer(f_detail).writerow([ds_name, kernel_options['name'], 
+				  train_examples, trial, 
+				  knn_options['n_neighbors'],
+				  len(gm_all), knn_options['test_size'], 
+				  accuracies[-1][0], accuracies[-1][1]])
+			f_detail.close()
+		
+	results = {}
+	results['ave_perf_train'] = np.mean([i[0] for i in accuracies], axis=0)
+	results['std_perf_train'] = np.std([i[0] for i in accuracies], axis=0, ddof=1)
+	results['ave_perf_test'] = np.mean([i[1] for i in accuracies], axis=0)
+	results['std_perf_test'] = np.std([i[1] for i in accuracies], axis=0, ddof=1)
+	
+	# write result summary for each letter. 
+	if save_results:
+		f_summary = open(dir_save + fn_output_summary, 'a')
+		csv.writer(f_summary).writerow([ds_name, kernel_options['name'], 
+				  train_examples, 
+				  knn_options['n_neighbors'],
+				  knn_options['test_size'], results['ave_perf_train'],
+				  results['ave_perf_test'], results['std_perf_train'],
+				  results['std_perf_test'], time_precompute_gm])
+		f_summary.close()
+	
+	
+def __kernel_knn_cv_trainset(dataset_all, ds_name, knn_options, kernel_options, gram_matrix_unnorm, time_precompute_gm, train_examples, save_results, dir_save, fn_output_detail, fn_output_summary):
+	y_all = dataset_all.targets
+	n_neighbors, n_splits, test_size = knn_options['n_neighbors'], knn_options['n_splits'], knn_options['test_size']
+	
+	# compute distance matrix.
+	gram_matrix = normalize_gram_matrix(gram_matrix_unnorm.copy())
+	dis_mat, _, _, _ = compute_distance_matrix(gram_matrix)
+
+	# get shuffles. 
+	train_indices, test_indices, _, _ = __get_shuffles(y_all, n_splits, test_size)
+			 
+	accuracies = []
+	for trial in range(len(train_indices)):
+		print('\ntrial =', trial)
+		
+		train_index = train_indices[trial]
+		test_index = test_indices[trial]
+		y_app = [y_all[i] for i in train_index]
+		y_test = [y_all[i] for i in test_index]
+		
+		N = len(train_index)
+		
+		d_app = dis_mat[train_index,:][:,train_index].copy()
+		
+		d_test = np.zeros((N, len(test_index)))
+		for i in range(N):
+			for j in range(len(test_index)):
+				d_test[i, j] = dis_mat[train_index[i], test_index[j]]
+				
+		accuracies.append(knn_classification(d_app, d_test, y_app, y_test, n_neighbors, verbose=True, text=train_examples))
+		
+		# write result detail.
+		if save_results:
+			print('writing results to files...')
+			f_detail = open(dir_save + fn_output_detail, 'a')
+			csv.writer(f_detail).writerow([ds_name, kernel_options['name'], 
+					  train_examples, trial, knn_options['n_neighbors'],
+					  len(gram_matrix), knn_options['test_size'], 
+					  accuracies[-1][0], accuracies[-1][1]])
+			f_detail.close()
+		
+	results = {}
+	results['ave_perf_train'] = np.mean([i[0] for i in accuracies], axis=0)
+	results['std_perf_train'] = np.std([i[0] for i in accuracies], axis=0, ddof=1)
+	results['ave_perf_test'] = np.mean([i[1] for i in accuracies], axis=0)
+	results['std_perf_test'] = np.std([i[1] for i in accuracies], axis=0, ddof=1)
+
+	# write result summary for each letter. 
+	if save_results:
+		f_summary = open(dir_save + fn_output_summary, 'a')
+		csv.writer(f_summary).writerow([ds_name, kernel_options['name'], 
+				  train_examples, knn_options['n_neighbors'],
+				  knn_options['test_size'], results['ave_perf_train'],
+				  results['ave_perf_test'], results['std_perf_train'],
+				  results['std_perf_test'], time_precompute_gm])
+		f_summary.close()
+	
+	
+def __get_shuffles(y_all, n_splits, test_size):
+	rs = ShuffleSplit(n_splits=n_splits, test_size=test_size, random_state=0)
+	train_indices = [[] for _ in range(n_splits)] 
+	test_indices = [[] for _ in range(n_splits)]
+	idx_targets = get_same_item_indices(y_all)
+	train_nums = []
+	keys = []
+	for key, item in idx_targets.items():
+		i = 0
+		for train_i, test_i in rs.split(item): # @todo: careful when parallel.
+			train_indices[i] += [item[idx] for idx in train_i]
+			test_indices[i] += [item[idx] for idx in test_i]
+			i += 1
+		train_nums.append(len(train_i))
+		keys.append(key)
+	return train_indices, test_indices, train_nums, keys
+	
+	
+def __generate_median_preimages(dataset, mpg_options, kernel_options, ged_options, mge_options):
+	mpg = MedianPreimageGenerator()
+	mpg.dataset = dataset.copy()
+	mpg.set_options(**mpg_options.copy())
+	mpg.kernel_options = kernel_options.copy()
+	mpg.ged_options = ged_options.copy()
+	mpg.mge_options = mge_options.copy()
+	mpg.run()
+	return mpg.set_median, mpg.gen_median
+
+
+def __get_gram_matrix(load_gm, dir_save, ds_name, kernel_options, dataset_all):
+	if load_gm == 'auto':
+		gm_fname = dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm.npz'
+		gmfile_exist = os.path.isfile(os.path.abspath(gm_fname))
+		if gmfile_exist:
+			gmfile = np.load(gm_fname, allow_pickle=True) # @todo: may not be safe.
+			gram_matrix_unnorm = gmfile['gram_matrix_unnorm']
+			time_precompute_gm = float(gmfile['run_time'])
+		else:
+			gram_matrix_unnorm, time_precompute_gm = __compute_gram_matrix_unnorm(dataset_all, kernel_options)
+			np.savez(dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm', gram_matrix_unnorm=gram_matrix_unnorm, run_time=time_precompute_gm)
+	elif not load_gm:
+		gram_matrix_unnorm, time_precompute_gm = __compute_gram_matrix_unnorm(dataset_all, kernel_options)
+		np.savez(dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm', gram_matrix_unnorm=gram_matrix_unnorm, run_time=time_precompute_gm)
+	else:
+		gm_fname = dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm.npz'
+		gmfile = np.load(gm_fname, allow_pickle=True)
+		gram_matrix_unnorm = gmfile['gram_matrix_unnorm']
+		time_precompute_gm = float(gmfile['run_time'])
+		
+	return gram_matrix_unnorm, time_precompute_gm
+
+
+def __get_graph_kernel(dataset, kernel_options):
+	from gklearn.utils.utils import get_graph_kernel_by_name
+	graph_kernel = get_graph_kernel_by_name(kernel_options['name'], 
+				  node_labels=dataset.node_labels,
+				  edge_labels=dataset.edge_labels, 
+				  node_attrs=dataset.node_attrs,
+				  edge_attrs=dataset.edge_attrs,
+				  ds_infos=dataset.get_dataset_infos(keys=['directed']),
+				  kernel_options=kernel_options)
+	return graph_kernel
+		
+		
+def __compute_gram_matrix_unnorm(dataset, kernel_options):
+	from gklearn.utils.utils import get_graph_kernel_by_name
+	graph_kernel = get_graph_kernel_by_name(kernel_options['name'], 
+				  node_labels=dataset.node_labels,
+				  edge_labels=dataset.edge_labels, 
+				  node_attrs=dataset.node_attrs,
+				  edge_attrs=dataset.edge_attrs,
+				  ds_infos=dataset.get_dataset_infos(keys=['directed']),
+				  kernel_options=kernel_options)
+	
+	gram_matrix, run_time = graph_kernel.compute(dataset.graphs, **kernel_options)
+	gram_matrix_unnorm = graph_kernel.gram_matrix_unnorm
+		
+	return gram_matrix_unnorm, run_time
+		
+		
+def __init_output_file_knn(ds_name, gkernel, fit_method, dir_output):
+	if not os.path.exists(dir_output):
+		os.makedirs(dir_output)
+	fn_output_detail = 'results_detail_knn.' + ds_name + '.' + gkernel + '.csv'
+	f_detail = open(dir_output + fn_output_detail, 'a')
+	csv.writer(f_detail).writerow(['dataset', 'graph kernel',
+			  'train examples', 'trial', 'num neighbors', 'num graphs', 'test size',
+			  'perf train', 'perf test'])
+	f_detail.close()
+	
+	fn_output_summary = 'results_summary_knn.' + ds_name + '.' + gkernel + '.csv'
+	f_summary = open(dir_output + fn_output_summary, 'a')
+	csv.writer(f_summary).writerow(['dataset', 'graph kernel',
+		      'train examples', 'num neighbors', 'test size',
+			  'ave perf train', 'ave perf test',
+			  'std perf train', 'std perf test', 'time precompute gm'])
+	f_summary.close()
+	
+	return fn_output_detail, fn_output_summary
\ No newline at end of file
diff --git a/gklearn/preimage/median_preimage_generator.py b/gklearn/preimage/median_preimage_generator.py
index fa1f4db..9deabe0 100644
--- a/gklearn/preimage/median_preimage_generator.py
+++ b/gklearn/preimage/median_preimage_generator.py
@@ -39,6 +39,8 @@ class MedianPreimageGenerator(PreimageGenerator):
 		self.__max_itrs_without_update = 3
 		self.__epsilon_residual = 0.01
 		self.__epsilon_ec = 0.1
+		self.__allow_zeros = False
+		self.__triangle_rule = True
 		# values to compute.
 		self.__runtime_optimize_ec = None
 		self.__runtime_generate_preimage = None
@@ -79,6 +81,8 @@ class MedianPreimageGenerator(PreimageGenerator):
 		self.__epsilon_ec = kwargs.get('epsilon_ec', 0.1)
 		self.__gram_matrix_unnorm = kwargs.get('gram_matrix_unnorm', None)
 		self.__runtime_precompute_gm = kwargs.get('runtime_precompute_gm', None)
+		self.__allow_zeros = kwargs.get('allow_zeros', False)
+		self.__triangle_rule = kwargs.get('triangle_rule', True)
 		
 		
 	def run(self):
@@ -277,7 +281,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 		options['edge_labels'] = self._dataset.edge_labels
 		options['node_attrs'] = self._dataset.node_attrs
 		options['edge_attrs'] = self._dataset.edge_attrs
-		ged_vec_init, ged_mat, n_edit_operations = compute_geds(graphs, options=options, parallel=self.__parallel)
+		ged_vec_init, ged_mat, n_edit_operations = compute_geds(graphs, options=options, parallel=self.__parallel, verbose=(self._verbose > 1))
 		residual_list = [np.sqrt(np.sum(np.square(np.array(ged_vec_init) - dis_k_vec)))]	
 		time_list = [time.time() - time0]
 		edit_cost_list = [self.__init_ecc]  
@@ -319,7 +323,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 			options['edge_labels'] = self._dataset.edge_labels
 			options['node_attrs'] = self._dataset.node_attrs
 			options['edge_attrs'] = self._dataset.edge_attrs
-			ged_vec, ged_mat, n_edit_operations = compute_geds(graphs, options=options, parallel=self.__parallel)
+			ged_vec, ged_mat, n_edit_operations = compute_geds(graphs, options=options, parallel=self.__parallel, verbose=(self._verbose > 1))
 			residual_list.append(np.sqrt(np.sum(np.square(np.array(ged_vec) - dis_k_vec))))
 			time_list.append(time.time() - time0)
 			edit_cost_list.append(self.__edit_cost_constants)
@@ -382,7 +386,8 @@ class MedianPreimageGenerator(PreimageGenerator):
 
 	def __update_ecc(self, nb_cost_mat, dis_k_vec, rw_constraints='inequality'):
 	#	if self.__ds_name == 'Letter-high':
-		if self.__ged_options['edit_cost'] == 'LETTER':			
+		if self.__ged_options['edit_cost'] == 'LETTER':
+			raise Exception('Cannot compute for cost "LETTER".')
 			pass
 	#		# method 1: set alpha automatically, just tune c_vir and c_eir by 
 	#		# LMS using cvxpy.
@@ -438,7 +443,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 	#			# 1. if c_vi != c_vr, c_ei != c_er.
 	#			nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 	#			x = cp.Variable(nb_cost_mat_new.shape[1])
-	#			cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+	#			cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 	##			# 1.1 no constraints.
 	##			constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])]]
 	#			# 1.2 c_vs <= c_vi + c_vr.
@@ -449,7 +454,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 	##			nb_cost_mat_new[:,0] += nb_cost_mat[:,1]
 	##			nb_cost_mat_new[:,2] += nb_cost_mat[:,5]
 	##			x = cp.Variable(nb_cost_mat_new.shape[1])
-	##			cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+	##			cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 	##			# 2.1 no constraints.
 	##			constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])]]
 	###			# 2.2 c_vs <= c_vi + c_vr.
@@ -461,35 +466,37 @@ class MedianPreimageGenerator(PreimageGenerator):
 	#			edit_costs_new = [x.value[0], x.value[0], x.value[1], x.value[2], x.value[2]]
 	#			edit_costs_new = np.array(edit_costs_new)
 	#			residual = np.sqrt(prob.value)
-			if rw_constraints == 'inequality':
-				# c_vs <= c_vi + c_vr.
+			if not self.__triangle_rule and self.__allow_zeros:
 				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 				x = cp.Variable(nb_cost_mat_new.shape[1])
-				cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
-				constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
-							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+				constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+							   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01]
 				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
 				self.__execute_cvx(prob)
 				edit_costs_new = x.value
 				residual = np.sqrt(prob.value)
-			elif rw_constraints == '2constraints':
-				# c_vs <= c_vi + c_vr and c_vi == c_vr, c_ei == c_er.
+			elif self.__triangle_rule and self.__allow_zeros:
 				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 				x = cp.Variable(nb_cost_mat_new.shape[1])
-				cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
-				constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
-							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0,
-							   np.array([1.0, -1.0, 0.0, 0.0, 0.0]).T@x == 0.0,
-							   np.array([0.0, 0.0, 0.0, 1.0, -1.0]).T@x == 0.0]
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+				constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+							   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01,
+							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
 				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
-				prob.solve()
+				self.__execute_cvx(prob)
 				edit_costs_new = x.value
 				residual = np.sqrt(prob.value)
-			elif rw_constraints == 'no-constraint':
-				# no constraint.
+			elif not self.__triangle_rule and not self.__allow_zeros:
 				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 				x = cp.Variable(nb_cost_mat_new.shape[1])
-				cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 				constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
 				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
 				prob.solve()
@@ -499,7 +506,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 	#				# c_vs <= c_vi + c_vr.
 	#				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 	#				x = cp.Variable(nb_cost_mat_new.shape[1])
-	#				cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+	#				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 	#				constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
 	#							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
 	#				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
@@ -508,15 +515,40 @@ class MedianPreimageGenerator(PreimageGenerator):
 	#				edit_costs_new = [x.value[0], x.value[0], x.value[1], x.value[2], x.value[2]]
 	#				edit_costs_new = np.array(edit_costs_new)
 	#				residual = np.sqrt(prob.value)
+			elif self.__triangle_rule and not self.__allow_zeros:
+				# c_vs <= c_vi + c_vr.
+				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
+				x = cp.Variable(nb_cost_mat_new.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+				constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
+							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				self.__execute_cvx(prob)
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)				
+			elif rw_constraints == '2constraints': # @todo: rearrange it later.
+				# c_vs <= c_vi + c_vr and c_vi == c_vr, c_ei == c_er.
+				nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
+				x = cp.Variable(nb_cost_mat_new.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+				constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
+							   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0,
+							   np.array([1.0, -1.0, 0.0, 0.0, 0.0]).T@x == 0.0,
+							   np.array([0.0, 0.0, 0.0, 1.0, -1.0]).T@x == 0.0]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				prob.solve()
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)
+
 		elif self.__ged_options['edit_cost'] == 'NON_SYMBOLIC':
 			is_n_attr = np.count_nonzero(nb_cost_mat[:,2])
 			is_e_attr = np.count_nonzero(nb_cost_mat[:,5])
 			
-			if self.__ds_name == 'SYNTHETICnew':
+			if self.__ds_name == 'SYNTHETICnew': # @todo: rearrenge this later.
 	#			nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
 				nb_cost_mat_new = nb_cost_mat[:,[2,3,4]]
 				x = cp.Variable(nb_cost_mat_new.shape[1])
-				cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+				cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 	#			constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
 	#						   np.array([0.0, 0.0, 0.0, 1.0, -1.0]).T@x == 0.0]
 	#			constraints = [x >= [0.0001 for i in range(nb_cost_mat_new.shape[1])]]
@@ -529,12 +561,154 @@ class MedianPreimageGenerator(PreimageGenerator):
 												 np.array([0.0])))
 				residual = np.sqrt(prob.value)
 				
-			elif rw_constraints == 'inequality':
+			elif not self.__triangle_rule and self.__allow_zeros:
+				if is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = x.value
+					residual = np.sqrt(prob.value)
+				elif is_n_attr and not is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value, np.array([0.0])))
+					residual = np.sqrt(prob.value)
+				elif not is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
+					residual = np.sqrt(prob.value)
+				else:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), 
+													 x.value[2:], np.array([0.0])))
+					residual = np.sqrt(prob.value)
+			elif self.__triangle_rule and self.__allow_zeros:
+				if is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+								   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
+								   np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = x.value
+					residual = np.sqrt(prob.value)
+				elif is_n_attr and not is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01,
+								   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value, np.array([0.0])))
+					residual = np.sqrt(prob.value)
+				elif not is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
+								   np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+								   np.array([0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
+					residual = np.sqrt(prob.value)
+				else:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), 
+													 x.value[2:], np.array([0.0])))
+					residual = np.sqrt(prob.value)
+			elif not self.__triangle_rule and not self.__allow_zeros:
+				if is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = x.value
+					residual = np.sqrt(prob.value)
+				elif is_n_attr and not is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value, np.array([0.0])))
+					residual = np.sqrt(prob.value)
+				elif not is_n_attr and is_e_attr:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
+					residual = np.sqrt(prob.value)
+				else:
+					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
+					x = cp.Variable(nb_cost_mat_new.shape[1])
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
+					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
+					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+					self.__execute_cvx(prob)
+					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), 
+													 x.value[2:], np.array([0.0])))
+					residual = np.sqrt(prob.value)
+			elif self.__triangle_rule and not self.__allow_zeros:
 				# c_vs <= c_vi + c_vr.
 				if is_n_attr and is_e_attr:
 					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
 					x = cp.Variable(nb_cost_mat_new.shape[1])
-					cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
 								   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
 								   np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
@@ -545,7 +719,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 				elif is_n_attr and not is_e_attr:
 					nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
 					x = cp.Variable(nb_cost_mat_new.shape[1])
-					cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
 								   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
 					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
@@ -555,7 +729,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 				elif not is_n_attr and is_e_attr:
 					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
 					x = cp.Variable(nb_cost_mat_new.shape[1])
-					cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
 								   np.array([0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
 					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
@@ -565,24 +739,61 @@ class MedianPreimageGenerator(PreimageGenerator):
 				else:
 					nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
 					x = cp.Variable(nb_cost_mat_new.shape[1])
-					cost_fun = cp.sum_squares(nb_cost_mat_new * x - dis_k_vec)
+					cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
 					constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
 					prob = cp.Problem(cp.Minimize(cost_fun), constraints)
 					self.__execute_cvx(prob)
 					edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), 
 													 x.value[2:], np.array([0.0])))
 					residual = np.sqrt(prob.value)
+
 		elif self.__ged_options['edit_cost'] == 'CONSTANT': # @todo: node/edge may not labeled.
-			x = cp.Variable(nb_cost_mat.shape[1])
-			cost_fun = cp.sum_squares(nb_cost_mat * x - dis_k_vec)
-			constraints = [x >= [0.01 for i in range(nb_cost_mat.shape[1])],
-						   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
-						   np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
-			prob = cp.Problem(cp.Minimize(cost_fun), constraints)
-			self.__execute_cvx(prob)
-			edit_costs_new = x.value
-			residual = np.sqrt(prob.value)
+			if not self.__triangle_rule and self.__allow_zeros:
+				x = cp.Variable(nb_cost_mat.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
+				constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
+							   np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				self.__execute_cvx(prob)
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)
+			elif self.__triangle_rule and self.__allow_zeros:
+				x = cp.Variable(nb_cost_mat.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
+				constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
+							   np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
+							   np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
+							   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
+							   np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				self.__execute_cvx(prob)
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)
+			elif not self.__triangle_rule and not self.__allow_zeros:
+				x = cp.Variable(nb_cost_mat.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
+				constraints = [x >= [0.01 for i in range(nb_cost_mat.shape[1])]]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				self.__execute_cvx(prob)
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)
+			elif self.__triangle_rule and not self.__allow_zeros:
+				x = cp.Variable(nb_cost_mat.shape[1])
+				cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
+				constraints = [x >= [0.01 for i in range(nb_cost_mat.shape[1])],
+							   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
+							   np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
+				prob = cp.Problem(cp.Minimize(cost_fun), constraints)
+				self.__execute_cvx(prob)
+				edit_costs_new = x.value
+				residual = np.sqrt(prob.value)
 		else:
+			raise Exception('The edit cost "', self.__ged_options['edit_cost'], '" is not supported for update progress.')
 	#	# method 1: simple least square method.
 	#	edit_costs_new, residual, _, _ = np.linalg.lstsq(nb_cost_mat, dis_k_vec,
 	#													 rcond=None)
@@ -607,7 +818,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 	#	G = -1 * np.identity(nb_cost_mat.shape[1])
 	#	h = np.array([0 for i in range(nb_cost_mat.shape[1])])
 			x = cp.Variable(nb_cost_mat.shape[1])
-			cost_fun = cp.sum_squares(nb_cost_mat * x - dis_k_vec)
+			cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
 			constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
 		#				   np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
 						   np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
@@ -669,6 +880,7 @@ class MedianPreimageGenerator(PreimageGenerator):
 		options = self.__mge_options.copy()
 		if not 'seed' in options:
 			options['seed'] = int(round(time.time() * 1000)) # @todo: may not work correctly for possible parallel usage.
+		options['parallel'] = self.__parallel
 		
 		# Select the GED algorithm.
 		self.__mge.set_options(mge_options_to_string(options))
@@ -676,8 +888,11 @@ class MedianPreimageGenerator(PreimageGenerator):
 					  edge_labels=self._dataset.edge_labels, 
 					  node_attrs=self._dataset.node_attrs, 
 					  edge_attrs=self._dataset.edge_attrs)
-		self.__mge.set_init_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
-		self.__mge.set_descent_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
+		ged_options = self.__ged_options.copy()
+		if self.__parallel:
+			ged_options['threads'] = 1
+		self.__mge.set_init_method(ged_options['method'], ged_options_to_string(ged_options))
+		self.__mge.set_descent_method(ged_options['method'], ged_options_to_string(ged_options))
 		
 		# Run the estimator.
 		self.__mge.run(graph_ids, set_median_id, gen_median_id)
diff --git a/gklearn/preimage/remove_best_graph.py b/gklearn/preimage/remove_best_graph.py
new file mode 100644
index 0000000..d6be2a6
--- /dev/null
+++ b/gklearn/preimage/remove_best_graph.py
@@ -0,0 +1,423 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wen May 27 14:27:15 2020
+
+@author: ljia
+"""
+import numpy as np
+import csv
+import os
+import os.path
+from gklearn.utils import Dataset
+from gklearn.preimage import MedianPreimageGenerator
+from gklearn.utils import normalize_gram_matrix
+from gklearn.utils import split_dataset_by_target
+from gklearn.preimage.utils import compute_k_dis
+from gklearn.utils.graphfiles import saveGXL
+import networkx as nx
+	
+
+def remove_best_graph(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=True, save_medians=True, plot_medians=True, load_gm='auto', dir_save='', irrelevant_labels=None, edge_required=False, cut_range=None):
+	"""Remove the best graph from the median set w.r.t. distance in kernel space, and to see if it is possible to generate the removed graph using the graphs left in the median set.
+	"""
+	# 1. get dataset.
+	print('1. getting dataset...')
+	dataset_all = Dataset()
+	dataset_all.load_predefined_dataset(ds_name)
+	dataset_all.trim_dataset(edge_required=edge_required)
+	if irrelevant_labels is not None:
+		dataset_all.remove_labels(**irrelevant_labels)
+	if cut_range is not None:
+		dataset_all.cut_graphs(cut_range)
+	datasets = split_dataset_by_target(dataset_all)
+
+	if save_results:
+		# create result files.
+		print('creating output files...')
+		fn_output_detail, fn_output_summary = __init_output_file(ds_name, kernel_options['name'], mpg_options['fit_method'], dir_save)
+	else:
+		fn_output_detail, fn_output_summary = None, None
+		
+	# 2. compute/load Gram matrix a priori.
+	print('2. computing/loading Gram matrix...')
+	gram_matrix_unnorm_list, time_precompute_gm_list = __get_gram_matrix(load_gm, dir_save, ds_name, kernel_options, datasets)
+		
+	sod_sm_list = []
+	sod_gm_list = []
+	dis_k_sm_list = []
+	dis_k_gm_list = []
+	dis_k_gi_min_list = []
+	time_optimize_ec_list = []
+	time_generate_list = []
+	time_total_list = []
+	itrs_list = []
+	converged_list = []
+	num_updates_ecc_list = []
+	mge_decrease_order_list = []
+	mge_increase_order_list = []
+	mge_converged_order_list = []
+	nb_sod_sm2gm = [0, 0, 0]
+	nb_dis_k_sm2gm = [0, 0, 0]
+	nb_dis_k_gi2sm = [0, 0, 0]
+	nb_dis_k_gi2gm = [0, 0, 0]
+	dis_k_max_list = []	
+	dis_k_min_list = []
+	dis_k_mean_list = []
+	best_dis_list = []
+	print('starting experiment for each class of target...')
+	idx_offset = 0
+	for idx, dataset in enumerate(datasets):
+		target = dataset.targets[0]
+		print('\ntarget =', target, '\n')
+#		if target != 1:
+# 			continue
+		
+		num_graphs = len(dataset.graphs)
+		if num_graphs < 2:
+			print('\nnumber of graphs = ', num_graphs, ', skip.\n')
+			idx_offset += 1
+			continue
+
+		# 3. get the best graph and remove it from median set.
+		print('3. getting and removing the best graph...')
+		gram_matrix_unnorm = gram_matrix_unnorm_list[idx - idx_offset]
+		best_index, best_dis, best_graph = __get_best_graph([g.copy() for g in dataset.graphs], normalize_gram_matrix(gram_matrix_unnorm.copy()))
+		median_set_new = [dataset.graphs[i] for i in range(len(dataset.graphs)) if i != best_index]
+		num_graphs -= 1
+		if num_graphs == 1:
+			continue		
+		best_dis_list.append(best_dis)
+		
+		dataset.load_graphs(median_set_new, targets=None)
+		gram_matrix_unnorm_new = np.delete(gram_matrix_unnorm, best_index, axis=0)
+		gram_matrix_unnorm_new = np.delete(gram_matrix_unnorm_new, best_index, axis=1)
+			
+		# 4. set parameters.
+		print('4. initializing mpg and setting parameters...')	
+		mpg_options['gram_matrix_unnorm'] = gram_matrix_unnorm_new
+		mpg_options['runtime_precompute_gm'] = time_precompute_gm_list[idx - idx_offset]
+		mpg = MedianPreimageGenerator()
+		mpg.dataset = dataset
+		mpg.set_options(**mpg_options.copy())
+		mpg.kernel_options = kernel_options.copy()
+		mpg.ged_options = ged_options.copy()
+		mpg.mge_options = mge_options.copy()
+
+		# 5. compute median preimage.
+		print('5. computing median preimage...')
+		mpg.run()
+		results = mpg.get_results()
+		
+		# 6. compute pairwise kernel distances.
+		print('6. computing pairwise kernel distances...')
+		_, dis_k_max, dis_k_min, dis_k_mean = mpg.graph_kernel.compute_distance_matrix()
+		dis_k_max_list.append(dis_k_max)
+		dis_k_min_list.append(dis_k_min)
+		dis_k_mean_list.append(dis_k_mean)
+		
+		# 7. save results (and median graphs).
+		print('7. saving results (and median graphs)...')
+		# write result detail.
+		if save_results:
+			print('writing results to files...')
+			sod_sm2gm = get_relations(np.sign(results['sod_gen_median'] - results['sod_set_median']))
+			dis_k_sm2gm = get_relations(np.sign(results['k_dis_gen_median'] - results['k_dis_set_median']))
+			dis_k_gi2sm = get_relations(np.sign(results['k_dis_set_median'] - results['k_dis_dataset']))
+			dis_k_gi2gm = get_relations(np.sign(results['k_dis_gen_median'] - results['k_dis_dataset']))
+
+			f_detail = open(dir_save + fn_output_detail, 'a')
+			csv.writer(f_detail).writerow([ds_name, kernel_options['name'], 
+					  ged_options['edit_cost'], ged_options['method'], 
+					  ged_options['attr_distance'], mpg_options['fit_method'], 
+					  num_graphs, target, 1, 
+					  results['sod_set_median'], results['sod_gen_median'],
+					  results['k_dis_set_median'], results['k_dis_gen_median'], 
+					  results['k_dis_dataset'], best_dis, best_index,
+					  sod_sm2gm, dis_k_sm2gm, 
+					  dis_k_gi2sm, dis_k_gi2gm,	results['edit_cost_constants'],
+					  results['runtime_precompute_gm'], results['runtime_optimize_ec'], 
+					  results['runtime_generate_preimage'], results['runtime_total'],
+					  results['itrs'], results['converged'],
+					  results['num_updates_ecc'],
+					  results['mge']['num_decrease_order'] > 0, # @todo: not suitable for multi-start mge
+					  results['mge']['num_increase_order'] > 0,
+					  results['mge']['num_converged_descents'] > 0])
+			f_detail.close()
+		
+			# compute result summary.
+			sod_sm_list.append(results['sod_set_median'])
+			sod_gm_list.append(results['sod_gen_median'])
+			dis_k_sm_list.append(results['k_dis_set_median'])
+			dis_k_gm_list.append(results['k_dis_gen_median'])
+			dis_k_gi_min_list.append(results['k_dis_dataset'])
+			time_precompute_gm_list.append(results['runtime_precompute_gm'])
+			time_optimize_ec_list.append(results['runtime_optimize_ec'])
+			time_generate_list.append(results['runtime_generate_preimage'])
+			time_total_list.append(results['runtime_total'])
+			itrs_list.append(results['itrs'])
+			converged_list.append(results['converged'])
+			num_updates_ecc_list.append(results['num_updates_ecc'])
+			mge_decrease_order_list.append(results['mge']['num_decrease_order'] > 0)
+			mge_increase_order_list.append(results['mge']['num_increase_order'] > 0)
+			mge_converged_order_list.append(results['mge']['num_converged_descents'] > 0)
+			# # SOD SM -> GM
+			if results['sod_set_median'] > results['sod_gen_median']:
+				nb_sod_sm2gm[0] += 1
+	#			repeats_better_sod_sm2gm.append(1)
+			elif results['sod_set_median'] == results['sod_gen_median']:
+				nb_sod_sm2gm[1] += 1
+			elif results['sod_set_median'] < results['sod_gen_median']:
+				nb_sod_sm2gm[2] += 1
+			# # dis_k SM -> GM
+			if results['k_dis_set_median'] > results['k_dis_gen_median']:
+				nb_dis_k_sm2gm[0] += 1
+	#			repeats_better_dis_k_sm2gm.append(1)
+			elif results['k_dis_set_median'] == results['k_dis_gen_median']:
+				nb_dis_k_sm2gm[1] += 1
+			elif results['k_dis_set_median'] < results['k_dis_gen_median']:
+				nb_dis_k_sm2gm[2] += 1
+			# # dis_k gi -> SM
+			if results['k_dis_dataset'] > results['k_dis_set_median']:
+				nb_dis_k_gi2sm[0] += 1
+	#			repeats_better_dis_k_gi2sm.append(1)
+			elif results['k_dis_dataset'] == results['k_dis_set_median']:
+				nb_dis_k_gi2sm[1] += 1
+			elif results['k_dis_dataset'] < results['k_dis_set_median']:
+				nb_dis_k_gi2sm[2] += 1
+			# # dis_k gi -> GM
+			if results['k_dis_dataset'] > results['k_dis_gen_median']:
+				nb_dis_k_gi2gm[0] += 1
+	#			repeats_better_dis_k_gi2gm.append(1)
+			elif results['k_dis_dataset'] == results['k_dis_gen_median']:
+				nb_dis_k_gi2gm[1] += 1
+			elif results['k_dis_dataset'] < results['k_dis_gen_median']:
+				nb_dis_k_gi2gm[2] += 1
+
+			# write result summary for each letter.
+			f_summary = open(dir_save + fn_output_summary, 'a')
+			csv.writer(f_summary).writerow([ds_name, kernel_options['name'], 
+					  ged_options['edit_cost'], ged_options['method'], 
+					  ged_options['attr_distance'], mpg_options['fit_method'], 
+					  num_graphs, target,
+					  results['sod_set_median'], results['sod_gen_median'],
+					  results['k_dis_set_median'], results['k_dis_gen_median'], 
+					  results['k_dis_dataset'], best_dis, best_index,
+					  sod_sm2gm, dis_k_sm2gm, 
+					  dis_k_gi2sm, dis_k_gi2gm, 
+					  results['runtime_precompute_gm'], results['runtime_optimize_ec'], 
+					  results['runtime_generate_preimage'], results['runtime_total'],
+					  results['itrs'], results['converged'],
+					  results['num_updates_ecc'], 
+					  results['mge']['num_decrease_order'] > 0, # @todo: not suitable for multi-start mge
+					  results['mge']['num_increase_order'] > 0,
+					  results['mge']['num_converged_descents'] > 0, 
+					  nb_sod_sm2gm, 
+					  nb_dis_k_sm2gm, nb_dis_k_gi2sm, nb_dis_k_gi2gm])
+			f_summary.close()
+			 
+		# save median graphs.
+		if save_medians:
+			if not os.path.exists(dir_save + 'medians/'):
+				os.makedirs(dir_save + 'medians/')
+			print('Saving median graphs to files...')
+			fn_pre_sm = dir_save + 'medians/set_median.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(mpg.set_median, fn_pre_sm + '.gxl', method='default', 
+					node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
+					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
+			fn_pre_gm = dir_save + 'medians/gen_median.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(mpg.gen_median, fn_pre_gm + '.gxl', method='default',
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
+					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
+			fn_best_dataset = dir_save + 'medians/g_best_dataset.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(best_graph, fn_best_dataset + '.gxl', method='default',
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
+					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
+			fn_best_median_set = dir_save + 'medians/g_best_median_set.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(mpg.best_from_dataset, fn_best_median_set + '.gxl', method='default',
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
+					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
+		
+		# plot median graphs.
+		if plot_medians and save_medians:
+			if ged_options['edit_cost'] == 'LETTER2' or ged_options['edit_cost'] == 'LETTER' or ds_name == 'Letter-high' or ds_name == 'Letter-med' or ds_name == 'Letter-low':			
+				draw_Letter_graph(mpg.set_median, fn_pre_sm)
+				draw_Letter_graph(mpg.gen_median, fn_pre_gm)
+				draw_Letter_graph(mpg.best_from_dataset, fn_best_dataset)
+
+	# write result summary for each letter. 
+	if save_results:
+		sod_sm_mean = np.mean(sod_sm_list)
+		sod_gm_mean = np.mean(sod_gm_list)
+		dis_k_sm_mean = np.mean(dis_k_sm_list)
+		dis_k_gm_mean = np.mean(dis_k_gm_list)
+		dis_k_gi_min_mean = np.mean(dis_k_gi_min_list)
+		best_dis_mean = np.mean(best_dis_list)
+		time_precompute_gm_mean = np.mean(time_precompute_gm_list)
+		time_optimize_ec_mean = np.mean(time_optimize_ec_list)
+		time_generate_mean = np.mean(time_generate_list)
+		time_total_mean = np.mean(time_total_list)
+		itrs_mean = np.mean(itrs_list)
+		num_converged = np.sum(converged_list)
+		num_updates_ecc_mean = np.mean(num_updates_ecc_list)
+		num_mge_decrease_order = np.sum(mge_decrease_order_list)
+		num_mge_increase_order = np.sum(mge_increase_order_list)
+		num_mge_converged = np.sum(mge_converged_order_list)
+		sod_sm2gm_mean = get_relations(np.sign(sod_gm_mean - sod_sm_mean))
+		dis_k_sm2gm_mean = get_relations(np.sign(dis_k_gm_mean - dis_k_sm_mean))
+		dis_k_gi2sm_mean = get_relations(np.sign(dis_k_sm_mean - dis_k_gi_min_mean))
+		dis_k_gi2gm_mean = get_relations(np.sign(dis_k_gm_mean - dis_k_gi_min_mean))
+		f_summary = open(dir_save + fn_output_summary, 'a')
+		csv.writer(f_summary).writerow([ds_name, kernel_options['name'], 
+				  ged_options['edit_cost'], ged_options['method'], 
+				  ged_options['attr_distance'], mpg_options['fit_method'], 
+				  num_graphs, 'all',
+				  sod_sm_mean, sod_gm_mean, dis_k_sm_mean, dis_k_gm_mean,
+				  dis_k_gi_min_mean, best_dis_mean, '-', 
+				  sod_sm2gm_mean, dis_k_sm2gm_mean, 
+				  dis_k_gi2sm_mean, dis_k_gi2gm_mean,
+				  time_precompute_gm_mean, time_optimize_ec_mean,
+				  time_generate_mean, time_total_mean, itrs_mean, 
+				  num_converged, num_updates_ecc_mean,
+				  num_mge_decrease_order, num_mge_increase_order,
+				  num_mge_converged])
+		f_summary.close()
+		
+	# save total pairwise kernel distances.
+	dis_k_max = np.max(dis_k_max_list)
+	dis_k_min = np.min(dis_k_min_list)
+	dis_k_mean = np.mean(dis_k_mean_list)
+	print('The maximum pairwise distance in kernel space:', dis_k_max)
+	print('The minimum pairwise distance in kernel space:', dis_k_min)
+	print('The average pairwise distance in kernel space:', dis_k_mean)
+
+	print('\ncomplete.\n')	
+
+
+def __get_best_graph(Gn, gram_matrix):
+	k_dis_list = []
+	for idx in range(len(Gn)):
+		k_dis_list.append(compute_k_dis(idx, range(0, len(Gn)), [1 / len(Gn)] * len(Gn), gram_matrix, withterm3=False))
+	best_index = np.argmin(k_dis_list)
+	best_dis = k_dis_list[best_index]
+	best_graph = Gn[best_index].copy()
+	return best_index, best_dis, best_graph 
+
+
+def get_relations(sign):
+	if sign == -1:
+		return 'better'
+	elif sign == 0:
+		return 'same'
+	elif sign == 1:
+		return 'worse'
+
+
+def __get_gram_matrix(load_gm, dir_save, ds_name, kernel_options, datasets):
+	if load_gm == 'auto':
+		gm_fname = dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm.npz'
+		gmfile_exist = os.path.isfile(os.path.abspath(gm_fname))
+		if gmfile_exist:
+			gmfile = np.load(gm_fname, allow_pickle=True) # @todo: may not be safe.
+			gram_matrix_unnorm_list = [item for item in gmfile['gram_matrix_unnorm_list']]
+			time_precompute_gm_list = gmfile['run_time_list'].tolist()
+		else:
+			gram_matrix_unnorm_list = []
+			time_precompute_gm_list = []
+			for dataset in datasets:
+				gram_matrix_unnorm, time_precompute_gm = __compute_gram_matrix_unnorm(dataset, kernel_options)
+				gram_matrix_unnorm_list.append(gram_matrix_unnorm)
+				time_precompute_gm_list.append(time_precompute_gm)
+			np.savez(dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm', gram_matrix_unnorm_list=gram_matrix_unnorm_list, run_time_list=time_precompute_gm_list)
+	elif not load_gm:
+		gram_matrix_unnorm_list = []
+		time_precompute_gm_list = []
+		for dataset in datasets:
+			gram_matrix_unnorm, time_precompute_gm = __compute_gram_matrix_unnorm(dataset, kernel_options)
+			gram_matrix_unnorm_list.append(gram_matrix_unnorm)
+			time_precompute_gm_list.append(time_precompute_gm)
+		np.savez(dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm', gram_matrix_unnorm_list=gram_matrix_unnorm_list, run_time_list=time_precompute_gm_list)
+	else:
+		gm_fname = dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm.npz'
+		gmfile = np.load(gm_fname, allow_pickle=True) # @todo: may not be safe.
+		gram_matrix_unnorm_list = [item for item in gmfile['gram_matrix_unnorm_list']]
+		time_precompute_gm_list = gmfile['run_time_list'].tolist()
+		
+	return gram_matrix_unnorm_list, time_precompute_gm_list
+
+
+def __get_graph_kernel(dataset, kernel_options):
+	from gklearn.utils.utils import get_graph_kernel_by_name
+	graph_kernel = get_graph_kernel_by_name(kernel_options['name'], 
+				  node_labels=dataset.node_labels,
+				  edge_labels=dataset.edge_labels, 
+				  node_attrs=dataset.node_attrs,
+				  edge_attrs=dataset.edge_attrs,
+				  ds_infos=dataset.get_dataset_infos(keys=['directed']),
+				  kernel_options=kernel_options)
+	return graph_kernel
+		
+		
+def __compute_gram_matrix_unnorm(dataset, kernel_options):
+	from gklearn.utils.utils import get_graph_kernel_by_name
+	graph_kernel = get_graph_kernel_by_name(kernel_options['name'], 
+				  node_labels=dataset.node_labels,
+				  edge_labels=dataset.edge_labels, 
+				  node_attrs=dataset.node_attrs,
+				  edge_attrs=dataset.edge_attrs,
+				  ds_infos=dataset.get_dataset_infos(keys=['directed']),
+				  kernel_options=kernel_options)
+	
+	gram_matrix, run_time = graph_kernel.compute(dataset.graphs, **kernel_options)
+	gram_matrix_unnorm = graph_kernel.gram_matrix_unnorm
+		
+	return gram_matrix_unnorm, run_time
+		
+		
+def __init_output_file(ds_name, gkernel, fit_method, dir_output):
+	if not os.path.exists(dir_output):
+		os.makedirs(dir_output)
+	fn_output_detail = 'results_detail.' + ds_name + '.' + gkernel + '.csv'
+	f_detail = open(dir_output + fn_output_detail, 'a')
+	csv.writer(f_detail).writerow(['dataset', 'graph kernel', 'edit cost', 
+			  'GED method', 'attr distance', 'fit method', 'num graphs', 
+			  'target', 'repeat', 'SOD SM', 'SOD GM', 'dis_k SM', 'dis_k GM',
+			  'min dis_k gi', 'best kernel dis', 'best graph index', 
+			  'SOD SM -> GM', 'dis_k SM -> GM', 'dis_k gi -> SM', 
+			  'dis_k gi -> GM', 'edit cost constants', 'time precompute gm',
+			  'time optimize ec', 'time generate preimage', 'time total',
+			  'itrs', 'converged', 'num updates ecc', 'mge decrease order', 
+			  'mge increase order', 'mge converged'])
+	f_detail.close()
+	
+	fn_output_summary = 'results_summary.' + ds_name + '.' + gkernel + '.csv'
+	f_summary = open(dir_output + fn_output_summary, 'a')
+	csv.writer(f_summary).writerow(['dataset', 'graph kernel', 'edit cost', 
+			  'GED method', 'attr distance', 'fit method', 'num graphs', 
+			  'target', 'SOD SM', 'SOD GM', 'dis_k SM', 'dis_k GM',
+			  'min dis_k gi', 'best kernel dis', 'best graph index',
+			  'SOD SM -> GM', 'dis_k SM -> GM', 'dis_k gi -> SM', 
+			  'dis_k gi -> GM', 'time precompute gm', 'time optimize ec', 
+			  'time generate preimage', 'time total', 'itrs', 'num converged', 
+			  'num updates ecc', 'mge num decrease order', 'mge num increase order', 
+			  'mge num converged', '# SOD SM -> GM', '# dis_k SM -> GM', 
+			  '# dis_k gi -> SM', '# dis_k gi -> GM'])
+	f_summary.close()
+	
+	return fn_output_detail, fn_output_summary
+
+
+#Dessin median courrant
+def draw_Letter_graph(graph, file_prefix):
+	import matplotlib
+	matplotlib.use('agg')
+	import matplotlib.pyplot as plt
+	plt.figure()
+	pos = {}
+	for n in graph.nodes:
+		pos[n] = np.array([float(graph.nodes[n]['x']),float(graph.nodes[n]['y'])])
+	nx.draw_networkx(graph, pos)
+	plt.savefig(file_prefix + '.eps', format='eps', dpi=300)
+#	plt.show()
+	plt.clf()
+	plt.close()
\ No newline at end of file
diff --git a/gklearn/preimage/utils.py b/gklearn/preimage/utils.py
index f99ab8a..5ca0c1e 100644
--- a/gklearn/preimage/utils.py
+++ b/gklearn/preimage/utils.py
@@ -45,7 +45,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 	if save_results:
 		# create result files.
 		print('creating output files...')
-		fn_output_detail, fn_output_summary = __init_output_file(ds_name, kernel_options['name'], mpg_options['fit_method'], dir_save)
+		fn_output_detail, fn_output_summary = __init_output_file_preimage(ds_name, kernel_options['name'], mpg_options['fit_method'], dir_save)
 		
 	sod_sm_list = []
 	sod_gm_list = []
@@ -82,22 +82,22 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 		gram_matrix_unnorm_list = []
 		time_precompute_gm_list = []
 	else:
-		gmfile = np.load()
-		gram_matrix_unnorm_list = gmfile['gram_matrix_unnorm_list']
-		time_precompute_gm_list = gmfile['run_time_list']
-# 	repeats_better_sod_sm2gm = []
-# 	repeats_better_dis_k_sm2gm = []
-# 	repeats_better_dis_k_gi2sm = []
-# 	repeats_better_dis_k_gi2gm = []
-		
+		gm_fname = dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm.npz'
+		gmfile = np.load(gm_fname, allow_pickle=True) # @todo: may not be safe.
+		gram_matrix_unnorm_list = [item for item in gmfile['gram_matrix_unnorm_list']]
+		time_precompute_gm_list = gmfile['run_time_list'].tolist()
+#	repeats_better_sod_sm2gm = []
+#	repeats_better_dis_k_sm2gm = []
+#	repeats_better_dis_k_gi2sm = []
+#	repeats_better_dis_k_gi2gm = []		
 		
-	print('start generating preimage for each class of target...')
+	print('starting generating preimage for each class of target...')
 	idx_offset = 0
 	for idx, dataset in enumerate(datasets):
 		target = dataset.targets[0]
 		print('\ntarget =', target, '\n')
-# 		if target != 1:
-#  			continue
+#		if target != 1:
+# 			continue
 		
 		num_graphs = len(dataset.graphs)
 		if num_graphs < 2:
@@ -148,7 +148,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 					  results['sod_set_median'], results['sod_gen_median'],
 					  results['k_dis_set_median'], results['k_dis_gen_median'], 
 					  results['k_dis_dataset'], sod_sm2gm, dis_k_sm2gm, 
-					  dis_k_gi2sm, dis_k_gi2gm, 	results['edit_cost_constants'],
+					  dis_k_gi2sm, dis_k_gi2gm,	results['edit_cost_constants'],
 					  results['runtime_precompute_gm'], results['runtime_optimize_ec'], 
 					  results['runtime_generate_preimage'], results['runtime_total'],
 					  results['itrs'], results['converged'],
@@ -177,7 +177,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			# # SOD SM -> GM
 			if results['sod_set_median'] > results['sod_gen_median']:
 				nb_sod_sm2gm[0] += 1
-	# 			repeats_better_sod_sm2gm.append(1)
+	#			repeats_better_sod_sm2gm.append(1)
 			elif results['sod_set_median'] == results['sod_gen_median']:
 				nb_sod_sm2gm[1] += 1
 			elif results['sod_set_median'] < results['sod_gen_median']:
@@ -185,7 +185,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			# # dis_k SM -> GM
 			if results['k_dis_set_median'] > results['k_dis_gen_median']:
 				nb_dis_k_sm2gm[0] += 1
-	# 			repeats_better_dis_k_sm2gm.append(1)
+	#			repeats_better_dis_k_sm2gm.append(1)
 			elif results['k_dis_set_median'] == results['k_dis_gen_median']:
 				nb_dis_k_sm2gm[1] += 1
 			elif results['k_dis_set_median'] < results['k_dis_gen_median']:
@@ -193,7 +193,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			# # dis_k gi -> SM
 			if results['k_dis_dataset'] > results['k_dis_set_median']:
 				nb_dis_k_gi2sm[0] += 1
-	# 			repeats_better_dis_k_gi2sm.append(1)
+	#			repeats_better_dis_k_gi2sm.append(1)
 			elif results['k_dis_dataset'] == results['k_dis_set_median']:
 				nb_dis_k_gi2sm[1] += 1
 			elif results['k_dis_dataset'] < results['k_dis_set_median']:
@@ -201,7 +201,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			# # dis_k gi -> GM
 			if results['k_dis_dataset'] > results['k_dis_gen_median']:
 				nb_dis_k_gi2gm[0] += 1
-	# 			repeats_better_dis_k_gi2gm.append(1)
+	#			repeats_better_dis_k_gi2gm.append(1)
 			elif results['k_dis_dataset'] == results['k_dis_gen_median']:
 				nb_dis_k_gi2gm[1] += 1
 			elif results['k_dis_dataset'] < results['k_dis_gen_median']:
@@ -225,7 +225,7 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 					  results['mge']['num_increase_order'] > 0,
 					  results['mge']['num_converged_descents'] > 0, 
 					  nb_sod_sm2gm, 
- 					  nb_dis_k_sm2gm, nb_dis_k_gi2sm, nb_dis_k_gi2gm])
+					  nb_dis_k_sm2gm, nb_dis_k_gi2sm, nb_dis_k_gi2gm])
 			f_summary.close()
 			 
 		# save median graphs.
@@ -235,15 +235,15 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			print('Saving median graphs to files...')
 			fn_pre_sm = dir_save + 'medians/set_median.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
 			saveGXL(mpg.set_median, fn_pre_sm + '.gxl', method='default', 
-					node_labels=dataset.node_labels, edge_labels=dataset.edge_labels, 	
+					node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
 					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
 			fn_pre_gm = dir_save + 'medians/gen_median.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
 			saveGXL(mpg.gen_median, fn_pre_gm + '.gxl', method='default',
-		   			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels, 	
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
 					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
 			fn_best_dataset = dir_save + 'medians/g_best_dataset.' + mpg_options['fit_method'] + '.nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
 			saveGXL(mpg.best_from_dataset, fn_best_dataset + '.gxl', method='default',
-		   			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels, 	
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
 					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
 		
 		# plot median graphs.
@@ -304,10 +304,10 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 	if (load_gm == 'auto' and not gmfile_exist) or not load_gm:
 		np.savez(dir_save + 'gram_matrix_unnorm.' + ds_name + '.' + kernel_options['name'] + '.gm', gram_matrix_unnorm_list=gram_matrix_unnorm_list, run_time_list=time_precompute_gm_list)	
 
-	print('\ncomplete.')	
+	print('\ncomplete.\n')	
 
 	
-def __init_output_file(ds_name, gkernel, fit_method, dir_output):
+def __init_output_file_preimage(ds_name, gkernel, fit_method, dir_output):
 	if not os.path.exists(dir_output):
 		os.makedirs(dir_output)
 #	fn_output_detail = 'results_detail.' + ds_name + '.' + gkernel + '.' + fit_method + '.csv'
@@ -335,9 +335,9 @@ def __init_output_file(ds_name, gkernel, fit_method, dir_output):
 			  'num updates ecc', 'mge num decrease order', 'mge num increase order', 
 			  'mge num converged', '# SOD SM -> GM', '# dis_k SM -> GM', 
 			  '# dis_k gi -> SM', '# dis_k gi -> GM'])
-# 			   'repeats better SOD SM -> GM', 
-# 			  'repeats better dis_k SM -> GM', 'repeats better dis_k gi -> SM', 
-# 			  'repeats better dis_k gi -> GM'])
+#			   'repeats better SOD SM -> GM', 
+#			  'repeats better dis_k SM -> GM', 'repeats better dis_k gi -> SM', 
+#			  'repeats better dis_k gi -> GM'])
 	f_summary.close()
 	
 	return fn_output_detail, fn_output_summary
@@ -462,6 +462,8 @@ def gram2distances(Kmatrix):
 
 def kernel_distance_matrix(Gn, node_label, edge_label, Kmatrix=None, 
 						   gkernel=None, verbose=True):
+	import warnings
+	warnings.warn('gklearn.preimage.utils.kernel_distance_matrix is deprecated, use gklearn.kernels.graph_kernel.compute_distance_matrix or gklearn.utils.compute_distance_matrix instead', DeprecationWarning)
 	dis_mat = np.empty((len(Gn), len(Gn)))
 	if Kmatrix is None:
 		Kmatrix = compute_kernel(Gn, gkernel, node_label, edge_label, verbose)
diff --git a/gklearn/tests/test_median_preimage_generator.py b/gklearn/tests/test_median_preimage_generator.py
new file mode 100644
index 0000000..c81bb7c
--- /dev/null
+++ b/gklearn/tests/test_median_preimage_generator.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jan 14 15:39:29 2020
+
+@author: ljia
+"""
+import multiprocessing
+import functools
+from gklearn.preimage.utils import generate_median_preimages_by_class
+
+		
+def test_median_preimage_generator():
+	"""MAO, Treelet, using CONSTANT, symbolic only.
+	"""
+	from gklearn.utils.kernels import polynomialkernel
+	# set parameters.
+	ds_name = 'MAO' #
+	mpg_options = {'fit_method': 'k-graphs',
+				   'init_ecc': [4, 4, 2, 1, 1, 1], #
+				   'ds_name': ds_name,
+				   'parallel': True, # False
+				   'time_limit_in_sec': 0,
+				   'max_itrs': 3, # 
+				   'max_itrs_without_update': 3,
+				   'epsilon_residual': 0.01,
+				   'epsilon_ec': 0.1,
+				   'verbose': 2}
+	pkernel = functools.partial(polynomialkernel, d=4, c=1e+7)
+	kernel_options = {'name': 'Treelet', #
+				      'sub_kernel': pkernel,
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 2}
+	ged_options = {'method': 'IPFP',
+				   'initialization_method': 'RANDOM', # 'NODE'
+				   'initial_solutions': 1, # 1
+				   'edit_cost': 'CONSTANT', # 
+				   'attr_distance': 'euclidean',
+				   'ratio_runs_from_initial_solutions': 1,
+				   'threads': multiprocessing.cpu_count(),
+				   'init_option': 'EAGER_WITHOUT_SHUFFLED_COPIES'}
+	mge_options = {'init_type': 'MEDOID',
+				   'random_inits': 10,
+				   'time_limit': 600,
+				   'verbose': 2,
+				   'refine': False}
+	save_results = True
+	dir_save = ds_name + '.' + kernel_options['name'] + '.symb.pytest/'
+	irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_stereo']} # 
+	edge_required = False #
+	
+	# print settings.
+	print('parameters:')
+	print('dataset name:', ds_name)
+	print('mpg_options:', mpg_options)
+	print('kernel_options:', kernel_options)
+	print('ged_options:', ged_options)
+	print('mge_options:', mge_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	for fit_method in ['k-graphs', 'expert', 'random']:
+		print('\n-------------------------------------')
+		print('fit method:', fit_method, '\n')
+		mpg_options['fit_method'] = fit_method
+		generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged_options, mge_options, save_results=save_results, save_medians=True, plot_medians=True, load_gm='auto', dir_save=dir_save, irrelevant_labels=irrelevant_labels, edge_required=edge_required, cut_range=range(0, 4))
\ No newline at end of file
diff --git a/gklearn/utils/__init__.py b/gklearn/utils/__init__.py
index 198bf75..af9c751 100644
--- a/gklearn/utils/__init__.py
+++ b/gklearn/utils/__init__.py
@@ -21,4 +21,6 @@ from gklearn.utils.timer import Timer
 from gklearn.utils.utils import get_graph_kernel_by_name
 from gklearn.utils.utils import compute_gram_matrices_by_class
 from gklearn.utils.utils import SpecialLabel
+from gklearn.utils.utils import normalize_gram_matrix, compute_distance_matrix
 from gklearn.utils.trie import Trie
+from gklearn.utils.knn import knn_cv, knn_classification
diff --git a/gklearn/utils/dataset.py b/gklearn/utils/dataset.py
index c499ce2..90bb886 100644
--- a/gklearn/utils/dataset.py
+++ b/gklearn/utils/dataset.py
@@ -522,6 +522,20 @@ class Dataset(object):
 		self.__targets = [self.__targets[i] for i in idx]
 		self.clean_labels()
 		
+		
+	def copy(self):
+		dataset = Dataset()
+		graphs = [g.copy() for g in self.__graphs] if self.__graphs is not None else None
+		target = self.__targets.copy() if self.__targets is not None else None
+		node_labels = self.__node_labels.copy() if self.__node_labels is not None else None
+		node_attrs = self.__node_attrs.copy() if self.__node_attrs is not None else None
+		edge_labels = self.__edge_labels.copy() if self.__edge_labels is not None else None
+		edge_attrs = self.__edge_attrs.copy() if self.__edge_attrs is not None else None
+		dataset.load_graphs(graphs, target)
+		dataset.set_labels(node_labels=node_labels, node_attrs=node_attrs, edge_labels=edge_labels, edge_attrs=edge_attrs)
+		# @todo: clean_labels and add other class members?
+		return dataset
+		
 	
 	def __get_dataset_size(self):
 		return len(self.__graphs)
@@ -721,7 +735,11 @@ def split_dataset_by_target(dataset):
 		sub_graphs = [graphs[i] for i in val]
 		sub_dataset = Dataset()
 		sub_dataset.load_graphs(sub_graphs, [key] * len(val))
-		sub_dataset.set_labels(node_labels=dataset.node_labels, node_attrs=dataset.node_attrs, edge_labels=dataset.edge_labels, edge_attrs=dataset.edge_attrs)
+		node_labels = dataset.node_labels.copy() if dataset.node_labels is not None else None
+		node_attrs = dataset.node_attrs.copy() if dataset.node_attrs is not None else None
+		edge_labels = dataset.edge_labels.copy() if dataset.edge_labels is not None else None
+		edge_attrs = dataset.edge_attrs.copy() if dataset.edge_attrs is not None else None
+		sub_dataset.set_labels(node_labels=node_labels, node_attrs=node_attrs, edge_labels=edge_labels, edge_attrs=edge_attrs)
 		datasets.append(sub_dataset)
 		# @todo: clean_labels?
 	return datasets
\ No newline at end of file
diff --git a/gklearn/utils/graph_files.py b/gklearn/utils/graph_files.py
index d977b73..7de4ba0 100644
--- a/gklearn/utils/graph_files.py
+++ b/gklearn/utils/graph_files.py
@@ -494,7 +494,8 @@ def load_tud(filename):
 					   'edge_labels': [], 'edge_attrs': []}
 		class_label_map = None
 		class_label_map_strings = []
-		content_rm = open(frm).read().splitlines()
+		with open(frm) as rm:
+			content_rm = rm.read().splitlines()
 		i = 0
 		while i < len(content_rm):
 			line = content_rm[i].strip()
@@ -558,16 +559,20 @@ def load_tud(filename):
 		label_names = {'node_labels': [], 'node_attrs': [], 
 					   'edge_labels': [], 'edge_attrs': []}
 		class_label_map = None
-
-	content_gi = open(fgi).read().splitlines()  # graph indicator
-	content_am = open(fam).read().splitlines()  # adjacency matrix
+	
+	with open(fgi) as gi:
+		content_gi = gi.read().splitlines()  # graph indicator
+	with open(fam) as am:
+		content_am = am.read().splitlines()  # adjacency matrix
 	
 	# load targets.
 	if 'fgl' in locals():
-		content_targets = open(fgl).read().splitlines()  # targets (classification)
+		with open(fgl) as gl:
+			content_targets = gl.read().splitlines()  # targets (classification)
 		targets = [float(i) for i in content_targets]
 	elif 'fga' in locals():
-		content_targets = open(fga).read().splitlines()  # targets (regression)
+		with open(fga) as ga:
+			content_targets = ga.read().splitlines()  # targets (regression)
 		targets = [int(i) for i in content_targets]
 	else:
 		raise Exception('Can not find targets file. Please make sure there is a "', ds_name, '_graph_labels.txt" or "', ds_name, '_graph_attributes.txt"', 'file in your dataset folder.')
@@ -577,7 +582,8 @@ def load_tud(filename):
 	# create graphs and add nodes
 	data = [nx.Graph(name=str(i)) for i in range(0, len(content_targets))]
 	if 'fnl' in locals():
-		content_nl = open(fnl).read().splitlines()  # node labels
+		with open(fnl) as nl:
+			content_nl = nl.read().splitlines()  # node labels
 		for idx, line in enumerate(content_gi):
 			# transfer to int first in case of unexpected blanks
 			data[int(line) - 1].add_node(idx)
@@ -605,7 +611,8 @@ def load_tud(filename):
 
 	# add edge labels
 	if 'fel' in locals():
-		content_el = open(fel).read().splitlines()
+		with open(fel) as el:
+			content_el = el.read().splitlines()
 		for idx, line in enumerate(content_el):
 			labels = [l.strip() for l in line.split(',')]
 			n = [int(i) - 1 for i in content_am[idx].split(',')]
@@ -621,7 +628,8 @@ def load_tud(filename):
 
 	# add node attributes
 	if 'fna' in locals():
-		content_na = open(fna).read().splitlines()
+		with open(fna) as na:
+			content_na = na.read().splitlines()
 		for idx, line in enumerate(content_na):
 			attrs = [a.strip() for a in line.split(',')]
 			g = int(content_gi[idx]) - 1
@@ -636,7 +644,8 @@ def load_tud(filename):
 
 	# add edge attributes
 	if 'fea' in locals():
-		content_ea = open(fea).read().splitlines()
+		with open(fea) as ea:
+			content_ea = ea.read().splitlines()
 		for idx, line in enumerate(content_ea):
 			attrs = [a.strip() for a in line.split(',')]
 			n = [int(i) - 1 for i in content_am[idx].split(',')]
@@ -669,7 +678,8 @@ def load_from_ds(filename, filename_targets):
 	data = []
 	y = []
 	label_names = {'node_labels': [], 'edge_labels': [], 'node_attrs': [], 'edge_attrs': []}
-	content = open(filename).read().splitlines()
+	with open(filename) as fn:
+		content = fn.read().splitlines()
 	extension = splitext(content[0].split(' ')[0])[1][1:]
 	if extension == 'ct':
 		load_file_fun = load_ct
@@ -691,8 +701,9 @@ def load_from_ds(filename, filename_targets):
 			g, l_names = load_file_fun(dirname_dataset + '/' + tmp.replace('#', '', 1))
 			data.append(g)
 			__append_label_names(label_names, l_names)
-															   
-		content_y = open(filename_targets).read().splitlines()
+		
+		with open(filename_targets) as fnt:
+			content_y = fnt.read().splitlines()
 		# assume entries in filename and filename_targets have the same order.
 		for item in content_y:
 			tmp = item.split(' ')
diff --git a/gklearn/utils/knn.py b/gklearn/utils/knn.py
new file mode 100644
index 0000000..81419be
--- /dev/null
+++ b/gklearn/utils/knn.py
@@ -0,0 +1,141 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon May 11 11:03:01 2020
+
+@author: ljia
+"""
+import numpy as np
+from sklearn.model_selection import ShuffleSplit
+from sklearn.neighbors import KNeighborsClassifier
+from sklearn.metrics import accuracy_score
+from gklearn.utils.utils import get_graph_kernel_by_name
+# from gklearn.preimage.utils import get_same_item_indices
+
+def sum_squares(a, b):
+	"""
+	Return the sum of squares of the difference between a and b, aka MSE
+	"""
+	return np.sum([(a[i] - b[i])**2 for i in range(len(a))])
+
+
+def euclid_d(x, y):
+	"""
+	1D euclidean distance
+	"""
+	return np.sqrt((x-y)**2)
+
+
+def man_d(x, y):
+	"""
+	1D manhattan distance
+	"""
+	return np.abs((x-y))
+
+
+def knn_regression(D_app, D_test, y_app, y_test, n_neighbors, verbose=True, text=None):
+
+	from sklearn.neighbors import KNeighborsRegressor
+	knn = KNeighborsRegressor(n_neighbors=n_neighbors, metric='precomputed')
+	knn.fit(D_app, y_app)
+	y_pred = knn.predict(D_app)
+	y_pred_test = knn.predict(D_test.T)
+	perf_app = np.sqrt(sum_squares(y_pred, y_app)/len(y_app))
+	perf_test = np.sqrt(sum_squares(y_pred_test, y_test)/len(y_test))
+
+	if (verbose):
+		print("Learning error with {} train examples : {}".format(text, perf_app))
+		print("Test error with {} train examples : {}".format(text, perf_test))
+
+	return perf_app, perf_test
+
+
+def knn_classification(d_app, d_test, y_app, y_test, n_neighbors, verbose=True, text=None):
+	knn = KNeighborsClassifier(n_neighbors=n_neighbors, metric='precomputed')
+	knn.fit(d_app, y_app)
+	y_pred = knn.predict(d_app)
+	y_pred_test = knn.predict(d_test.T)
+	perf_app = accuracy_score(y_app, y_pred)
+	perf_test = accuracy_score(y_test, y_pred_test)
+
+	if (verbose):
+		print("Learning accuracy with {} costs : {}".format(text, perf_app))
+		print("Test accuracy with {} costs : {}".format(text, perf_test))
+		
+	return perf_app, perf_test
+	
+
+def knn_cv(dataset, kernel_options, trainset=None, n_neighbors=1, n_splits=50, test_size=0.9, verbose=True):
+	'''
+	Perform a knn classification cross-validation on given dataset.
+	'''
+# 	Gn = dataset.graphs
+	y_all = dataset.targets
+	
+	# compute kernel distances.
+	dis_mat = __compute_kernel_distances(dataset, kernel_options, trainset=trainset)
+		
+	
+	rs = ShuffleSplit(n_splits=n_splits, test_size=test_size, random_state=0)
+# 	train_indices = [[] for _ in range(n_splits)] 
+# 	test_indices = [[] for _ in range(n_splits)]
+# 	idx_targets = get_same_item_indices(y_all)
+# 	for key, item in idx_targets.items():
+# 		i = 0
+# 		for train_i, test_i in rs.split(item): # @todo: careful when parallel.
+# 			train_indices[i] += [item[idx] for idx in train_i]
+# 			test_indices[i] += [item[idx] for idx in test_i]
+# 			i += 1
+	
+	accuracies = []
+# 	for trial in range(len(train_indices)):
+# 		train_index = train_indices[trial]
+# 		test_index = test_indices[trial] 
+	for train_index, test_index in rs.split(y_all):
+# 		print(train_index, test_index)
+# 		G_app = [Gn[i] for i in train_index]
+# 		G_test = [Gn[i] for i in test_index]
+		y_app = [y_all[i] for i in train_index]
+		y_test = [y_all[i] for i in test_index]
+		
+		N = len(train_index)
+		
+		d_app = dis_mat.copy()
+		d_app = d_app[train_index,:]
+		d_app = d_app[:,train_index]
+		
+		d_test = np.zeros((N, len(test_index)))
+		
+		for i in range(N):
+			for j in range(len(test_index)):
+				d_test[i, j] = dis_mat[train_index[i], test_index[j]]
+				
+		accuracies.append(knn_classification(d_app, d_test, y_app, y_test, n_neighbors, verbose=verbose, text=''))
+		
+	results = {}
+	results['ave_perf_train'] = np.mean([i[0] for i in accuracies], axis=0)
+	results['std_perf_train'] = np.std([i[0] for i in accuracies], axis=0, ddof=1)
+	results['ave_perf_test'] = np.mean([i[1] for i in accuracies], axis=0)
+	results['std_perf_test'] = np.std([i[1] for i in accuracies], axis=0, ddof=1)
+
+	return results
+		
+		
+def __compute_kernel_distances(dataset, kernel_options, trainset=None):
+	graph_kernel = get_graph_kernel_by_name(kernel_options['name'], 
+				  node_labels=dataset.node_labels,
+				  edge_labels=dataset.edge_labels, 
+				  node_attrs=dataset.node_attrs,
+				  edge_attrs=dataset.edge_attrs,
+				  ds_infos=dataset.get_dataset_infos(keys=['directed']),
+				  kernel_options=kernel_options)
+	
+	gram_matrix, run_time = graph_kernel.compute(dataset.graphs, **kernel_options)
+
+	dis_mat, _, _, _ = graph_kernel.compute_distance_matrix()
+	
+	if trainset is not None:
+		gram_matrix_unnorm = graph_kernel.gram_matrix_unnorm
+		
+
+	return dis_mat
\ No newline at end of file
diff --git a/gklearn/utils/utils.py b/gklearn/utils/utils.py
index 9223b7a..868f0f6 100644
--- a/gklearn/utils/utils.py
+++ b/gklearn/utils/utils.py
@@ -1,7 +1,7 @@
 import networkx as nx
 import numpy as np
 from copy import deepcopy
-from enum import Enum, auto
+from enum import Enum, unique
 #from itertools import product
 
 # from tqdm import tqdm
@@ -468,7 +468,36 @@ def get_mlti_dim_edge_attrs(G, attr_names):
 	return attributes
 
 
+@unique
 class SpecialLabel(Enum):
-    """can be used to define special labels.
-    """
-    DUMMY = auto # The dummy label.
\ No newline at end of file
+	"""can be used to define special labels.
+	"""
+	DUMMY = 1 # The dummy label.
+	# DUMMY = auto # enum.auto does not exist in Python 3.5.
+	
+	
+def normalize_gram_matrix(gram_matrix):
+	diag = gram_matrix.diagonal().copy()
+	for i in range(len(gram_matrix)):
+		for j in range(i, len(gram_matrix)):
+			gram_matrix[i][j] /= np.sqrt(diag[i] * diag[j])
+			gram_matrix[j][i] = gram_matrix[i][j]
+	return gram_matrix
+	
+	
+def compute_distance_matrix(gram_matrix):
+	dis_mat = np.empty((len(gram_matrix), len(gram_matrix)))
+	for i in range(len(gram_matrix)):
+		for j in range(i, len(gram_matrix)):
+			dis = gram_matrix[i, i] + gram_matrix[j, j] - 2 * gram_matrix[i, j]
+			if dis < 0:
+				if dis > -1e-10:
+					dis = 0
+				else:
+					raise ValueError('The distance is negative.')
+			dis_mat[i, j] = np.sqrt(dis)
+			dis_mat[j, i] = dis_mat[i, j]
+	dis_max = np.max(np.max(dis_mat))
+	dis_min = np.min(np.min(dis_mat[dis_mat != 0]))
+	dis_mean = np.mean(np.mean(dis_mat))
+	return dis_mat, dis_max, dis_min, dis_mean
\ No newline at end of file
diff --git a/requirements.txt b/requirements.txt
index 85aabf8..24d6efe 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,10 +1,11 @@
-numpy>=1.15.2
+numpy>=1.16.2
 scipy>=1.1.0
 matplotlib>=3.0.0
 networkx>=2.2
 scikit-learn>=0.20.0
 tabulate>=0.8.2
 tqdm>=4.26.0
-# cvxpy # for preimage.
-# cvxopt # for preimage.
-# mosek # for preimage.
+cvxpy>=1.0.31 # for preimage. Does not work for "pip install graphkit-learn".
+# -e https://files.pythonhosted.org/packages/11/d0/d900870dc2d02ea74961b90c353666c6528a33ea61a10aa59a0d5574ae59/cvxpy-1.0.31.tar.gz # for preimage.
+cvxopt>=1.2.5 # for preimage.
+mosek>=9.2.5; python_version >= '3.6' # for preimage.
diff --git a/requirements_pypi.txt b/requirements_pypi.txt
new file mode 100644
index 0000000..f4854fc
--- /dev/null
+++ b/requirements_pypi.txt
@@ -0,0 +1,11 @@
+numpy>=1.16.2
+scipy>=1.1.0
+matplotlib>=3.0.0
+networkx>=2.2
+scikit-learn>=0.20.0
+tabulate>=0.8.2
+tqdm>=4.26.0
+# cvxpy>=1.0.31 # for preimage. Does not work for "pip install graphkit-learn".
+# -e https://files.pythonhosted.org/packages/11/d0/d900870dc2d02ea74961b90c353666c6528a33ea61a10aa59a0d5574ae59/cvxpy-1.0.31.tar.gz # for preimage.
+cvxopt>=1.2.5 # for preimage.
+mosek>=9.2.5; python_version >= '3.6' # for preimage.
diff --git a/setup.py b/setup.py
index 0d7fbba..a84679e 100644
--- a/setup.py
+++ b/setup.py
@@ -3,15 +3,15 @@ import setuptools
 with open("README.md", "r") as fh:
     long_description = fh.read()
 
-with open('requirements.txt') as fp:
+with open('requirements_pypi.txt') as fp:
     install_requires = fp.read()
 
 setuptools.setup(
     name="graphkit-learn",
-    version="0.2b1",
+    version="0.2b2",
     author="Linlin Jia",
     author_email="linlin.jia@insa-rouen.fr",
-    description="A Python library for graph kernels based on linear patterns",
+    description="A Python library for graph kernels, graph edit distances, and graph pre-images",
     long_description=long_description,
     long_description_content_type="text/markdown",
     url="https://github.com/jajupmochi/graphkit-learn",