diff --git a/gklearn/preimage/__init__.py b/gklearn/preimage/__init__.py
index 385762e..7972820 100644
--- a/gklearn/preimage/__init__.py
+++ b/gklearn/preimage/__init__.py
@@ -14,3 +14,4 @@ from gklearn.preimage.preimage_generator import PreimageGenerator
 from gklearn.preimage.median_preimage_generator import MedianPreimageGenerator
 from gklearn.preimage.random_preimage_generator import RandomPreimageGenerator
 from gklearn.preimage.kernel_knn_cv import kernel_knn_cv
+from gklearn.preimage.generate_random_preimages_by_class import generate_random_preimages_by_class
diff --git a/gklearn/preimage/experiments/xp_random_preimage.py b/gklearn/preimage/experiments/xp_random_preimage.py
new file mode 100644
index 0000000..8700ad8
--- /dev/null
+++ b/gklearn/preimage/experiments/xp_random_preimage.py
@@ -0,0 +1,1192 @@
+#!/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 import generate_random_preimages_by_class
+from gklearn.utils import compute_gram_matrices_by_class
+
+
+dir_root = '../results/xp_random_preimage/'
+
+
+def xp_median_preimage_15_1():
+	"""xp 15_1: AIDS, StructuralSP, using CONSTANT, symbolic only.
+	"""
+	# set parameters.
+	ds_name = 'AIDS' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/'
+	irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y'], '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'AIDS' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y'], '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+ 
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	from gklearn.utils.kernels import polynomialkernel
+	# set parameters.
+	ds_name = 'AIDS' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y'], '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'AIDS' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 2}
+	kernel_options = {'name': 'WeisfeilerLehman',
+				      'height': 10,
+					  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['chem', 'charge', 'x', 'y'], '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('kernel_options:', kernel_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.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'DD' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'PAH' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'PAH' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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
+	# set parameters.
+	ds_name = 'PAH' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'PAH' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 2}
+	kernel_options = {'name': 'WeisfeilerLehman',
+				      'height': 14,
+					  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 0}
+	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('kernel_options:', kernel_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.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'PAH' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MAO' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_type', '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MAO' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_type', '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	from gklearn.utils.kernels import polynomialkernel
+	# set parameters.
+	ds_name = 'MAO' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_type', '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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MAO' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 2}
+	kernel_options = {'name': 'WeisfeilerLehman',
+				      'height': 6,
+					  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '.symb/' 
+	irrelevant_labels = {'node_attrs': ['x', 'y', 'z'], 'edge_labels': ['bond_type', '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('kernel_options:', kernel_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.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'Monoterpenoides' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'Monoterpenoides' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	from gklearn.utils.kernels import polynomialkernel
+	# set parameters.
+	ds_name = 'Monoterpenoides' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 0}
+	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}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'Monoterpenoides' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 2}
+	kernel_options = {'name': 'WeisfeilerLehman',
+				      'height': 4,
+					  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MUTAG' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	irrelevant_labels = {'edge_labels': ['label_0']} #
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MUTAG' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	irrelevant_labels = {'edge_labels': ['label_0']} #
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	from gklearn.utils.kernels import polynomialkernel
+	# set parameters.
+	ds_name = 'MUTAG' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   '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': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	irrelevant_labels = {'edge_labels': ['label_0']} #
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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.
+	"""
+	# set parameters.
+	ds_name = 'MUTAG' #
+	rpg_options = {'k': 5,
+				   'r_max': 10, #
+				   'l': 500,
+				   'alphas': None,
+				   'parallel': True,
+				   'verbose': 2}
+	kernel_options = {'name': 'WeisfeilerLehman',
+				      'height': 1,
+					  'base_kernel': 'subtree',
+ 					  'parallel': 'imap_unordered', 
+                      # 'parallel': None, 
+					  'n_jobs': multiprocessing.cpu_count(),
+					  'normalize': True,
+					  'verbose': 0}
+	save_results = True
+	dir_save = dir_root + ds_name + '.' + kernel_options['name'] + '/' 
+	irrelevant_labels = {'edge_labels': ['label_0']} #
+	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('kernel_options:', kernel_options)
+	print('save_results:', save_results)
+	print('irrelevant_labels:', irrelevant_labels)
+	print()
+	
+	# generate preimages.
+	try:
+		generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=save_results, save_preimages=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))
+				
+				
+if __name__ == "__main__":
+
+# 	#### 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 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 14_1: DD, PathUpToH, using CONSTANT.
+ 	xp_median_preimage_14_1()
diff --git a/gklearn/preimage/generate_random_preimages_by_class.py b/gklearn/preimage/generate_random_preimages_by_class.py
new file mode 100644
index 0000000..656579f
--- /dev/null
+++ b/gklearn/preimage/generate_random_preimages_by_class.py
@@ -0,0 +1,188 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Jun  1 17:02:51 2020
+
+@author: ljia
+"""
+
+import numpy as np
+from gklearn.utils import Dataset
+import csv
+import os
+import os.path
+from gklearn.preimage import RandomPreimageGenerator
+from gklearn.utils import split_dataset_by_target
+from gklearn.utils.graphfiles import saveGXL
+
+
+def generate_random_preimages_by_class(ds_name, rpg_options, kernel_options, save_results=True, save_preimages=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)
+	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_preimage(ds_name, kernel_options['name'], dir_save)
+		
+
+	dis_k_dataset_list = []
+	dis_k_preimage_list = []
+	time_precompute_gm_list = []
+	time_generate_list = []
+	time_total_list = []
+	itrs_list = []
+	num_updates_list = []
+	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 = []
+	elif not load_gm:
+		gram_matrix_unnorm_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()	
+		
+	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
+		
+		num_graphs = len(dataset.graphs)
+		if num_graphs < 2:
+			print('\nnumber of graphs = ', num_graphs, ', skip.\n')
+			idx_offset += 1
+			continue
+			
+		# 2. set parameters.
+		print('2. initializing mpg and setting parameters...')
+		if load_gm:
+			if gmfile_exist:
+				rpg_options['gram_matrix_unnorm'] = gram_matrix_unnorm_list[idx - idx_offset]
+				rpg_options['runtime_precompute_gm'] = time_precompute_gm_list[idx - idx_offset]
+		rpg = RandomPreimageGenerator()
+		rpg.dataset = dataset
+		rpg.set_options(**rpg_options.copy())
+		rpg.kernel_options = kernel_options.copy()
+
+		# 3. compute preimage.
+		print('3. computing preimage...')
+		rpg.run()
+		results = rpg.get_results()
+		
+		# 4. save results (and median graphs).
+		print('4. saving results (and preimages)...')
+		# 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'], 
+					  num_graphs, target, 1, 
+					  results['k_dis_dataset'], results['k_dis_preimage'],
+					  results['runtime_precompute_gm'], 
+					  results['runtime_generate_preimage'], results['runtime_total'],
+					  results['itrs'], results['num_updates']])
+			f_detail.close()
+		
+			# compute result summary.
+			dis_k_dataset_list.append(results['k_dis_dataset'])
+			dis_k_preimage_list.append(results['k_dis_preimage'])
+			time_precompute_gm_list.append(results['runtime_precompute_gm'])
+			time_generate_list.append(results['runtime_generate_preimage'])
+			time_total_list.append(results['runtime_total'])
+			itrs_list.append(results['itrs'])
+			num_updates_list.append(results['num_updates'])
+			
+			# 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'], 
+					  num_graphs, target,
+					  results['k_dis_dataset'], results['k_dis_preimage'],
+					  results['runtime_precompute_gm'], 
+					  results['runtime_generate_preimage'], results['runtime_total'],
+					  results['itrs'], results['num_updates']])
+			f_summary.close()
+			 
+		# save median graphs.
+		if save_preimages:
+			if not os.path.exists(dir_save + 'preimages/'):
+				os.makedirs(dir_save + 'preimages/')
+			print('Saving preimages to files...')
+			fn_best_dataset = dir_save + 'preimages/g_best_dataset.' + 'nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(rpg.best_from_dataset, 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_preimage = dir_save + 'preimages/g_preimage.' + 'nbg' + str(num_graphs) + '.y' + str(target) + '.repeat' + str(1)
+			saveGXL(rpg.preimage, fn_preimage + '.gxl', method='default',
+		  			node_labels=dataset.node_labels, edge_labels=dataset.edge_labels,	
+					node_attrs=dataset.node_attrs, edge_attrs=dataset.edge_attrs)
+				
+		if (load_gm == 'auto' and not gmfile_exist) or not load_gm:
+			gram_matrix_unnorm_list.append(rpg.gram_matrix_unnorm)
+
+	# write result summary for each class. 
+	if save_results:
+		dis_k_dataset_mean = np.mean(dis_k_dataset_list)
+		dis_k_preimage_mean = np.mean(dis_k_preimage_list)
+		time_precompute_gm_mean = np.mean(time_precompute_gm_list)
+		time_generate_mean = np.mean(time_generate_list)
+		time_total_mean = np.mean(time_total_list)
+		itrs_mean = np.mean(itrs_list)
+		num_updates_mean = np.mean(num_updates_list)
+		f_summary = open(dir_save + fn_output_summary, 'a')
+		csv.writer(f_summary).writerow([ds_name, kernel_options['name'],
+				  num_graphs, 'all',
+				  dis_k_dataset_mean, dis_k_preimage_mean,
+				  time_precompute_gm_mean,
+				  time_generate_mean, time_total_mean, itrs_mean, 
+				  num_updates_mean])
+		f_summary.close()
+	
+	# write Gram matrices to file.
+	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.\n')	
+
+	
+def __init_output_file_preimage(ds_name, gkernel, 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', 'num graphs', 
+			  'target', 'repeat', 'dis_k best from dataset', 'dis_k preimage',
+			  'time precompute gm', 'time generate preimage', 'time total',
+			  'itrs', 'num updates'])
+	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', 'num graphs', 
+			  'target', 'dis_k best from dataset', 'dis_k preimage',
+			  'time precompute gm', 'time generate preimage', 'time total',
+			  'itrs', 'num updates'])
+	f_summary.close()
+	
+	return fn_output_detail, fn_output_summary
\ No newline at end of file
diff --git a/gklearn/preimage/utils.py b/gklearn/preimage/utils.py
index 5ca0c1e..6bc10c7 100644
--- a/gklearn/preimage/utils.py
+++ b/gklearn/preimage/utils.py
@@ -256,7 +256,7 @@ 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:
 			gram_matrix_unnorm_list.append(mpg.gram_matrix_unnorm)
 
-	# write result summary for each letter. 
+	# write result summary for each class. 
 	if save_results:
 		sod_sm_mean = np.mean(sod_sm_list)
 		sod_gm_mean = np.mean(sod_gm_list)