graphkit-learn/gklearn/kernels/weisfeiler_lehman.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Apr 14 15:16:34 2020

@author: ljia

@references:

	[1] Shervashidze N, Schweitzer P, Leeuwen EJ, Mehlhorn K, Borgwardt KM.
	Weisfeiler-lehman graph kernels. Journal of Machine Learning Research.
	2011;12(Sep):2539-61.
"""

import numpy as np
import networkx as nx
from collections import Counter
# from functools import partial
from gklearn.utils import SpecialLabel
from gklearn.utils.parallel import parallel_gm, parallel_me
from gklearn.kernels import GraphKernel


class WeisfeilerLehman(GraphKernel): # @todo: sp, edge user kernel.

	def __init__(self, **kwargs):
		GraphKernel.__init__(self)
		self._node_labels = kwargs.get('node_labels', [])
		self._edge_labels = kwargs.get('edge_labels', [])
		self._height = int(kwargs.get('height', 0))
		self._base_kernel = kwargs.get('base_kernel', 'subtree')
		self._ds_infos = kwargs.get('ds_infos', {})


	def _compute_gm_series(self):
# 		if self._verbose >= 2:
# 			import warnings
# 			warnings.warn('A part of the computation is parallelized.')

		self._add_dummy_node_labels(self._graphs)

		# for WL subtree kernel
		if self._base_kernel == 'subtree':
			gram_matrix = self._subtree_kernel_do(self._graphs)

		# for WL shortest path kernel
		elif self._base_kernel == 'sp':
			gram_matrix = self._sp_kernel_do(self._graphs)

		# for WL edge kernel
		elif self._base_kernel == 'edge':
			gram_matrix = self._edge_kernel_do(self._graphs)

		# for user defined base kernel
		else:
			gram_matrix = self._user_kernel_do(self._graphs)

		return gram_matrix


	def _compute_gm_imap_unordered(self):
		self._add_dummy_node_labels(self._graphs)

		if self._base_kernel == 'subtree':
			gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))

			def init_worker(gn_toshare):
				global G_gn
				G_gn = gn_toshare
			do_fun = self._wrapper_pairwise
			parallel_gm(do_fun, gram_matrix, self._graphs, init_worker=init_worker,
			  glbv=(self._graphs,), n_jobs=self._n_jobs, verbose=self._verbose)
			return gram_matrix
		else:
			if self._verbose >= 2:
				import warnings
				warnings.warn('This base kernel is not parallelized. The serial computation is used instead.')
			return self._compute_gm_series()


	def _compute_kernel_list_series(self, g1, g_list): # @todo: this should be better.
# 		if self._verbose >= 2:
# 			import warnings
# 			warnings.warn('A part of the computation is parallelized.')

		self._add_dummy_node_labels(g_list + [g1])

		# for WL subtree kernel
		if self._base_kernel == 'subtree':
			gram_matrix = self._subtree_kernel_do(g_list + [g1])

		# for WL shortest path kernel
		elif self._base_kernel == 'sp':
			gram_matrix = self._sp_kernel_do(g_list + [g1])

		# for WL edge kernel
		elif self._base_kernel == 'edge':
			gram_matrix = self._edge_kernel_do(g_list + [g1])

		# for user defined base kernel
		else:
			gram_matrix = self._user_kernel_do(g_list + [g1])

		return list(gram_matrix[-1][0:-1])


	def _compute_kernel_list_imap_unordered(self, g1, g_list):
		self._add_dummy_node_labels(g_list + [g1])

		if self._base_kernel == 'subtree':
			kernel_list = [None] * len(g_list)

			def init_worker(g1_toshare, g_list_toshare):
				global G_g1, G_g_list
				G_g1 = g1_toshare
				G_g_list = g_list_toshare
			do_fun = self._wrapper_kernel_list_do
			def func_assign(result, var_to_assign):
				var_to_assign[result[0]] = result[1]
			itr = range(len(g_list))
			len_itr = len(g_list)
			parallel_me(do_fun, func_assign, kernel_list, itr, len_itr=len_itr,
				init_worker=init_worker, glbv=(g1, g_list), method='imap_unordered',
				n_jobs=self._n_jobs, itr_desc='Computing kernels', verbose=self._verbose)
			return kernel_list
		else:
			if self._verbose >= 2:
				import warnings
				warnings.warn('This base kernel is not parallelized. The serial computation is used instead.')
			return self._compute_kernel_list_series(g1, g_list)


	def _wrapper_kernel_list_do(self, itr):
		return self._kernel_do_exp(G_g1, G_g_list[itr])


	def _compute_single_kernel_series(self, g1, g2):  # @todo: this should be better.
		self._add_dummy_node_labels([g1] + [g2])

		# for WL subtree kernel
		if self._base_kernel == 'subtree':
			gram_matrix = self._subtree_kernel_do([g1] + [g2])

		# for WL shortest path kernel
		elif self._base_kernel == 'sp':
			gram_matrix = self._sp_kernel_do([g1] + [g2])

		# for WL edge kernel
		elif self._base_kernel == 'edge':
			gram_matrix = self._edge_kernel_do([g1] + [g2])

		# for user defined base kernel
		else:
			gram_matrix = self._user_kernel_do([g1] + [g2])

		return gram_matrix[0][1]


	def pairwise_kernel(self, g1, g2):
		Gn = [g1, g2]
		kernel = 0

		# initial for height = 0
		all_num_of_each_label = [] # number of occurence of each label in each graph in this iteration

		# for each graph
		for G in Gn:
			# set all labels into a tuple.
			for nd, attrs in G.nodes(data=True): # @todo: there may be a better way.
				G.nodes[nd]['label_tuple'] = tuple(attrs[name] for name in self._node_labels)
			# get the set of original labels
			labels_ori = list(nx.get_node_attributes(G, 'label_tuple').values())
			# number of occurence of each label in G
			all_num_of_each_label.append(dict(Counter(labels_ori)))

		# Compute subtree kernel with the 0th iteration and add it to the final kernel.
		kernel = self._compute_kernel_itr(kernel, all_num_of_each_label)

		# iterate each height
		for h in range(1, self._height + 1):
			all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration
			num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs
	#		all_labels_ori = set() # all unique orignal labels in all graphs in this iteration
			all_num_of_each_label = [] # number of occurence of each label in G

			# @todo: parallel this part.
			for idx, G in enumerate(Gn):

				all_multisets = []
				for node, attrs in G.nodes(data=True):
					# Multiset-label determination.
					multiset = [G.nodes[neighbors]['label_tuple'] for neighbors in G[node]]
					# sorting each multiset
					multiset.sort()
					multiset = [attrs['label_tuple']] + multiset # add the prefix
					all_multisets.append(tuple(multiset))

				# label compression
				set_unique = list(set(all_multisets)) # set of unique multiset labels
				# a dictionary mapping original labels to new ones.
				set_compressed = {}
				# if a label occured before, assign its former compressed label,
				# else assign the number of labels occured + 1 as the compressed label.
				for value in set_unique:
					if value in all_set_compressed.keys():
						set_compressed.update({value: all_set_compressed[value]})
					else:
						set_compressed.update({value: str(num_of_labels_occured + 1)})
						num_of_labels_occured += 1

				all_set_compressed.update(set_compressed)

				# relabel nodes
				for idx, node in enumerate(G.nodes()):
					G.nodes[node]['label_tuple'] = set_compressed[all_multisets[idx]]

				# get the set of compressed labels
				labels_comp = list(nx.get_node_attributes(G, 'label_tuple').values())
	#			all_labels_ori.update(labels_comp)
				all_num_of_each_label.append(dict(Counter(labels_comp)))

			# Compute subtree kernel with h iterations and add it to the final kernel
			kernel = self._compute_kernel_itr(kernel, all_num_of_each_label)

		return kernel


	def _wrapper_pairwise(self, itr):
		i = itr[0]
		j = itr[1]
		return i, j, self.pairwise_kernel(G_gn[i], G_gn[j])


	def _compute_kernel_itr(kernel, all_num_of_each_label):
		labels = set(list(all_num_of_each_label[0].keys()) +
			   list(all_num_of_each_label[1].keys()))
		vector1 = np.array([(all_num_of_each_label[0][label]
							if (label in all_num_of_each_label[0].keys()) else 0)
							for label in labels])
		vector2 = np.array([(all_num_of_each_label[1][label]
							if (label in all_num_of_each_label[1].keys()) else 0)
							for label in labels])
		kernel += np.dot(vector1, vector2)
		return kernel


	def _subtree_kernel_do(self, Gn):
		"""Compute Weisfeiler-Lehman kernels between graphs.

		Parameters
		----------
		Gn : List of NetworkX graph
			List of graphs between which the kernels are computed.

		Return
		------
		gram_matrix : Numpy matrix
			Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs.
		"""
		gram_matrix = np.zeros((len(Gn), len(Gn)))

		# initial for height = 0
		all_num_of_each_label = [] # number of occurence of each label in each graph in this iteration

		# for each graph
		for G in Gn:
			# set all labels into a tuple.
			for nd, attrs in G.nodes(data=True): # @todo: there may be a better way.
				G.nodes[nd]['label_tuple'] = tuple(attrs[name] for name in self._node_labels)
			# get the set of original labels
			labels_ori = list(nx.get_node_attributes(G, 'label_tuple').values())
			# number of occurence of each label in G
			all_num_of_each_label.append(dict(Counter(labels_ori)))

		# Compute subtree kernel with the 0th iteration and add it to the final kernel.
		self._compute_gram_itr(gram_matrix, all_num_of_each_label)

		# iterate each height
		for h in range(1, self._height + 1):
			all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration
			num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs
	#		all_labels_ori = set() # all unique orignal labels in all graphs in this iteration
			all_num_of_each_label = [] # number of occurence of each label in G

			# @todo: parallel this part.
			for idx, G in enumerate(Gn):

				all_multisets = []
				for node, attrs in G.nodes(data=True):
					# Multiset-label determination.
					multiset = [G.nodes[neighbors]['label_tuple'] for neighbors in G[node]]
					# sorting each multiset
					multiset.sort()
					multiset = [attrs['label_tuple']] + multiset # add the prefix
					all_multisets.append(tuple(multiset))

				# label compression
				set_unique = list(set(all_multisets)) # set of unique multiset labels
				# a dictionary mapping original labels to new ones.
				set_compressed = {}
				# if a label occured before, assign its former compressed label,
				# else assign the number of labels occured + 1 as the compressed label.
				for value in set_unique:
					if value in all_set_compressed.keys():
						set_compressed.update({value: all_set_compressed[value]})
					else:
						set_compressed.update({value: str(num_of_labels_occured + 1)})
						num_of_labels_occured += 1

				all_set_compressed.update(set_compressed)

				# relabel nodes
				for idx, node in enumerate(G.nodes()):
					G.nodes[node]['label_tuple'] = set_compressed[all_multisets[idx]]

				# get the set of compressed labels
				labels_comp = list(nx.get_node_attributes(G, 'label_tuple').values())
	#			all_labels_ori.update(labels_comp)
				all_num_of_each_label.append(dict(Counter(labels_comp)))

			# Compute subtree kernel with h iterations and add it to the final kernel
			self._compute_gram_itr(gram_matrix, all_num_of_each_label)

		return gram_matrix


	def _compute_gram_itr(self, gram_matrix, all_num_of_each_label):
		"""Compute Gram matrix using the base kernel.
		"""
# 		if self._parallel == 'imap_unordered':
# 			# compute kernels.
# 			def init_worker(alllabels_toshare):
# 				global G_alllabels
# 				G_alllabels = alllabels_toshare
# 			do_partial = partial(self._wrapper_compute_subtree_kernel, gram_matrix)
# 			parallel_gm(do_partial, gram_matrix, Gn, init_worker=init_worker,
# 						glbv=(all_num_of_each_label,), n_jobs=self._n_jobs, verbose=self._verbose)
# 		elif self._parallel is None:
		for i in range(len(gram_matrix)):
			for j in range(i, len(gram_matrix)):
				gram_matrix[i][j] = self._compute_subtree_kernel(all_num_of_each_label[i],
					   all_num_of_each_label[j], gram_matrix[i][j])
				gram_matrix[j][i] = gram_matrix[i][j]


	def _compute_subtree_kernel(self, num_of_each_label1, num_of_each_label2, kernel):
		"""Compute the subtree kernel.
		"""
		labels = set(list(num_of_each_label1.keys()) + list(num_of_each_label2.keys()))
		vector1 = np.array([(num_of_each_label1[label]
							if (label in num_of_each_label1.keys()) else 0)
							for label in labels])
		vector2 = np.array([(num_of_each_label2[label]
							if (label in num_of_each_label2.keys()) else 0)
							for label in labels])
		kernel += np.dot(vector1, vector2)
		return kernel


# 	def _wrapper_compute_subtree_kernel(self, gram_matrix, itr):
# 		i = itr[0]
# 		j = itr[1]
# 		return i, j, self._compute_subtree_kernel(G_alllabels[i], G_alllabels[j], gram_matrix[i][j])


	def _wl_spkernel_do(Gn, node_label, edge_label, height):
		"""Compute Weisfeiler-Lehman shortest path kernels between graphs.

		Parameters
		----------
		Gn : List of NetworkX graph
			List of graphs between which the kernels are computed.
		node_label : string
			node attribute used as label.
		edge_label : string
			edge attribute used as label.
		height : int
			subtree height.

		Return
		------
		gram_matrix : Numpy matrix
			Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs.
		"""
		pass
		from gklearn.utils.utils import getSPGraph

		# init.
		height = int(height)
		gram_matrix = np.zeros((len(Gn), len(Gn))) # init kernel

		Gn = [ getSPGraph(G, edge_weight = edge_label) for G in Gn ] # get shortest path graphs of Gn

		# initial for height = 0
		for i in range(0, len(Gn)):
			for j in range(i, len(Gn)):
				for e1 in Gn[i].edges(data = True):
					for e2 in Gn[j].edges(data = True):
						if e1[2]['cost'] != 0 and e1[2]['cost'] == e2[2]['cost'] and ((e1[0] == e2[0] and e1[1] == e2[1]) or (e1[0] == e2[1] and e1[1] == e2[0])):
							gram_matrix[i][j] += 1
				gram_matrix[j][i] = gram_matrix[i][j]

		# iterate each height
		for h in range(1, height + 1):
			all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration
			num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs
			for G in Gn: # for each graph
				set_multisets = []
				for node in G.nodes(data = True):
					# Multiset-label determination.
					multiset = [ G.node[neighbors][node_label] for neighbors in G[node[0]] ]
					# sorting each multiset
					multiset.sort()
					multiset = node[1][node_label] + ''.join(multiset) # concatenate to a string and add the prefix
					set_multisets.append(multiset)

				# label compression
				set_unique = list(set(set_multisets)) # set of unique multiset labels
				# a dictionary mapping original labels to new ones.
				set_compressed = {}
				# if a label occured before, assign its former compressed label, else assign the number of labels occured + 1 as the compressed label
				for value in set_unique:
					if value in all_set_compressed.keys():
						set_compressed.update({ value : all_set_compressed[value] })
					else:
						set_compressed.update({ value : str(num_of_labels_occured + 1) })
						num_of_labels_occured += 1

				all_set_compressed.update(set_compressed)

				# relabel nodes
				for node in G.nodes(data = True):
					node[1][node_label] = set_compressed[set_multisets[node[0]]]

			# Compute subtree kernel with h iterations and add it to the final kernel
			for i in range(0, len(Gn)):
				for j in range(i, len(Gn)):
					for e1 in Gn[i].edges(data = True):
						for e2 in Gn[j].edges(data = True):
							if e1[2]['cost'] != 0 and e1[2]['cost'] == e2[2]['cost'] and ((e1[0] == e2[0] and e1[1] == e2[1]) or (e1[0] == e2[1] and e1[1] == e2[0])):
								gram_matrix[i][j] += 1
					gram_matrix[j][i] = gram_matrix[i][j]

		return gram_matrix



	def _wl_edgekernel_do(Gn, node_label, edge_label, height):
		"""Compute Weisfeiler-Lehman edge kernels between graphs.

		Parameters
		----------
		Gn : List of NetworkX graph
			List of graphs between which the kernels are computed.
		node_label : string
			node attribute used as label.
		edge_label : string
			edge attribute used as label.
		height : int
			subtree height.

		Return
		------
		gram_matrix : Numpy matrix
			Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs.
		"""
		pass
		# init.
		height = int(height)
		gram_matrix = np.zeros((len(Gn), len(Gn))) # init kernel

		# initial for height = 0
		for i in range(0, len(Gn)):
			for j in range(i, len(Gn)):
				for e1 in Gn[i].edges(data = True):
					for e2 in Gn[j].edges(data = True):
						if e1[2][edge_label] == e2[2][edge_label] and ((e1[0] == e2[0] and e1[1] == e2[1]) or (e1[0] == e2[1] and e1[1] == e2[0])):
							gram_matrix[i][j] += 1
				gram_matrix[j][i] = gram_matrix[i][j]

		# iterate each height
		for h in range(1, height + 1):
			all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration
			num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs
			for G in Gn: # for each graph
				set_multisets = []
				for node in G.nodes(data = True):
					# Multiset-label determination.
					multiset = [ G.node[neighbors][node_label] for neighbors in G[node[0]] ]
					# sorting each multiset
					multiset.sort()
					multiset = node[1][node_label] + ''.join(multiset) # concatenate to a string and add the prefix
					set_multisets.append(multiset)

				# label compression
				set_unique = list(set(set_multisets)) # set of unique multiset labels
				# a dictionary mapping original labels to new ones.
				set_compressed = {}
				# if a label occured before, assign its former compressed label, else assign the number of labels occured + 1 as the compressed label
				for value in set_unique:
					if value in all_set_compressed.keys():
						set_compressed.update({ value : all_set_compressed[value] })
					else:
						set_compressed.update({ value : str(num_of_labels_occured + 1) })
						num_of_labels_occured += 1

				all_set_compressed.update(set_compressed)

				# relabel nodes
				for node in G.nodes(data = True):
					node[1][node_label] = set_compressed[set_multisets[node[0]]]

			# Compute subtree kernel with h iterations and add it to the final kernel
			for i in range(0, len(Gn)):
				for j in range(i, len(Gn)):
					for e1 in Gn[i].edges(data = True):
						for e2 in Gn[j].edges(data = True):
							if e1[2][edge_label] == e2[2][edge_label] and ((e1[0] == e2[0] and e1[1] == e2[1]) or (e1[0] == e2[1] and e1[1] == e2[0])):
								gram_matrix[i][j] += 1
					gram_matrix[j][i] = gram_matrix[i][j]

		return gram_matrix


	def _wl_userkernel_do(Gn, node_label, edge_label, height, base_kernel):
		"""Compute Weisfeiler-Lehman kernels based on user-defined kernel between graphs.

		Parameters
		----------
		Gn : List of NetworkX graph
			List of graphs between which the kernels are computed.
		node_label : string
			node attribute used as label.
		edge_label : string
			edge attribute used as label.
		height : int
			subtree height.
		base_kernel : string
			Name of the base kernel function used in each iteration of WL kernel. This function returns a Numpy matrix, each element of which is the user-defined Weisfeiler-Lehman kernel between 2 praphs.

		Return
		------
		gram_matrix : Numpy matrix
			Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs.
		"""
		pass
		# init.
		height = int(height)
		gram_matrix = np.zeros((len(Gn), len(Gn))) # init kernel

		# initial for height = 0
		gram_matrix = base_kernel(Gn, node_label, edge_label)

		# iterate each height
		for h in range(1, height + 1):
			all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration
			num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs
			for G in Gn: # for each graph
				set_multisets = []
				for node in G.nodes(data = True):
					# Multiset-label determination.
					multiset = [ G.node[neighbors][node_label] for neighbors in G[node[0]] ]
					# sorting each multiset
					multiset.sort()
					multiset = node[1][node_label] + ''.join(multiset) # concatenate to a string and add the prefix
					set_multisets.append(multiset)

				# label compression
				set_unique = list(set(set_multisets)) # set of unique multiset labels
				# a dictionary mapping original labels to new ones.
				set_compressed = {}
				# if a label occured before, assign its former compressed label, else assign the number of labels occured + 1 as the compressed label
				for value in set_unique:
					if value in all_set_compressed.keys():
						set_compressed.update({ value : all_set_compressed[value] })
					else:
						set_compressed.update({ value : str(num_of_labels_occured + 1) })
						num_of_labels_occured += 1

				all_set_compressed.update(set_compressed)

				# relabel nodes
				for node in G.nodes(data = True):
					node[1][node_label] = set_compressed[set_multisets[node[0]]]

			# Compute kernel with h iterations and add it to the final kernel
			gram_matrix += base_kernel(Gn, node_label, edge_label)

		return gram_matrix


	def _add_dummy_node_labels(self, Gn):
		if len(self._node_labels) == 0 or (len(self._node_labels) == 1 and self._node_labels[0] == SpecialLabel.DUMMY):
			for i in range(len(Gn)):
				nx.set_node_attributes(Gn[i], '0', SpecialLabel.DUMMY)
			self._node_labels = [SpecialLabel.DUMMY]


class WLSubtree(WeisfeilerLehman):

	def __init__(self, **kwargs):
		kwargs['base_kernel'] = 'subtree'
		super().__init__(**kwargs)