""" @author: linlin @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 sys import pathlib from collections import Counter sys.path.insert(0, "../") import networkx as nx import numpy as np import time from gklearn.kernels.pathKernel import pathkernel def weisfeilerlehmankernel(*args, node_label = 'atom', edge_label = 'bond_type', height = 0, base_kernel = 'subtree'): """Calculate Weisfeiler-Lehman kernels between graphs. Parameters ---------- Gn : List of NetworkX graph List of graphs between which the kernels are calculated. / G1, G2 : NetworkX graphs 2 graphs between which the kernel is calculated. node_label : string node attribute used as label. The default node label is atom. edge_label : string edge attribute used as label. The default edge label is bond_type. height : int subtree height base_kernel : string base kernel used in each iteration of WL kernel. The default base kernel is subtree kernel. For user-defined kernel, base_kernel is the 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 ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs. Notes ----- This function now supports WL subtree kernel, WL shortest path kernel and WL edge kernel. """ base_kernel = base_kernel.lower() Gn = args[0] if len(args) == 1 else [args[0], args[1]] # arrange all graphs in a list Kmatrix = np.zeros((len(Gn), len(Gn))) start_time = time.time() # for WL subtree kernel if base_kernel == 'subtree': Kmatrix = _wl_subtreekernel_do(args[0], node_label, edge_label, height) # for WL shortest path kernel elif base_kernel == 'sp': Kmatrix = _wl_spkernel_do(args[0], node_label, edge_label, height) # for WL edge kernel elif base_kernel == 'edge': Kmatrix = _wl_edgekernel_do(args[0], node_label, edge_label, height) # for user defined base kernel else: Kmatrix = _wl_userkernel_do(args[0], node_label, edge_label, height, base_kernel) run_time = time.time() - start_time print("\n --- Weisfeiler-Lehman %s kernel matrix of size %d built in %s seconds ---" % (base_kernel, len(args[0]), run_time)) return Kmatrix, run_time def _wl_subtreekernel_do(Gn, node_label, edge_label, height): """Calculate Weisfeiler-Lehman subtree kernels between graphs. Parameters ---------- Gn : List of NetworkX graph List of graphs between which the kernels are calculated. node_label : string node attribute used as label. edge_label : string edge attribute used as label. height : int subtree height. Return ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs. """ height = int(height) Kmatrix = np.zeros((len(Gn), len(Gn))) all_num_of_labels_occured = 0 # number of the set of letters that occur before as node labels at least once in all graphs # initial for height = 0 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 each graph in this iteration all_set_compressed = {} # a dictionary mapping original labels to new ones in all graphs in this iteration num_of_labels_occured = all_num_of_labels_occured # number of the set of letters that occur before as node labels at least once in all graphs # for each graph for G in Gn: # get the set of original labels labels_ori = list(nx.get_node_attributes(G, node_label).values()) all_labels_ori.update(labels_ori) num_of_each_label = dict(Counter(labels_ori)) # number of occurence of each label in graph all_num_of_each_label.append(num_of_each_label) num_of_labels = len(num_of_each_label) # number of all unique labels all_labels_ori.update(labels_ori) all_num_of_labels_occured += len(all_labels_ori) # calculate subtree kernel with the 0th iteration and add it to the final kernel for i in range(0, len(Gn)): for j in range(i, len(Gn)): labels = set(list(all_num_of_each_label[i].keys()) + list(all_num_of_each_label[j].keys())) vector1 = np.matrix([ (all_num_of_each_label[i][label] if (label in all_num_of_each_label[i].keys()) else 0) for label in labels ]) vector2 = np.matrix([ (all_num_of_each_label[j][label] if (label in all_num_of_each_label[j].keys()) else 0) for label in labels ]) Kmatrix[i][j] += np.dot(vector1, vector2.transpose()) Kmatrix[j][i] = Kmatrix[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 = all_num_of_labels_occured # number of the set of letters that occur before as node labels at least once in all graphs all_labels_ori = set() all_num_of_each_label = [] # for each graph for idx, G in enumerate(Gn): 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]]] # get the set of compressed labels labels_comp = list(nx.get_node_attributes(G, node_label).values()) all_labels_ori.update(labels_comp) num_of_each_label = dict(Counter(labels_comp)) all_num_of_each_label.append(num_of_each_label) all_num_of_labels_occured += len(all_labels_ori) # calculate 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)): labels = set(list(all_num_of_each_label[i].keys()) + list(all_num_of_each_label[j].keys())) vector1 = np.matrix([ (all_num_of_each_label[i][label] if (label in all_num_of_each_label[i].keys()) else 0) for label in labels ]) vector2 = np.matrix([ (all_num_of_each_label[j][label] if (label in all_num_of_each_label[j].keys()) else 0) for label in labels ]) Kmatrix[i][j] += np.dot(vector1, vector2.transpose()) Kmatrix[j][i] = Kmatrix[i][j] return Kmatrix def _wl_spkernel_do(Gn, node_label, edge_label, height): """Calculate Weisfeiler-Lehman shortest path kernels between graphs. Parameters ---------- Gn : List of NetworkX graph List of graphs between which the kernels are calculated. node_label : string node attribute used as label. edge_label : string edge attribute used as label. height : int subtree height. Return ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs. """ from gklearn.utils.utils import getSPGraph # init. height = int(height) Kmatrix = 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])): Kmatrix[i][j] += 1 Kmatrix[j][i] = Kmatrix[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]]] # calculate 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])): Kmatrix[i][j] += 1 Kmatrix[j][i] = Kmatrix[i][j] return Kmatrix def _wl_edgekernel_do(Gn, node_label, edge_label, height): """Calculate Weisfeiler-Lehman edge kernels between graphs. Parameters ---------- Gn : List of NetworkX graph List of graphs between which the kernels are calculated. node_label : string node attribute used as label. edge_label : string edge attribute used as label. height : int subtree height. Return ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs. """ # init. height = int(height) Kmatrix = 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])): Kmatrix[i][j] += 1 Kmatrix[j][i] = Kmatrix[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]]] # calculate 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])): Kmatrix[i][j] += 1 Kmatrix[j][i] = Kmatrix[i][j] return Kmatrix def _wl_userkernel_do(Gn, node_label, edge_label, height, base_kernel): """Calculate Weisfeiler-Lehman kernels based on user-defined kernel between graphs. Parameters ---------- Gn : List of NetworkX graph List of graphs between which the kernels are calculated. 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 ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the Weisfeiler-Lehman kernel between 2 praphs. """ # init. height = int(height) Kmatrix = np.zeros((len(Gn), len(Gn))) # init kernel # initial for height = 0 Kmatrix = 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]]] # calculate kernel with h iterations and add it to the final kernel Kmatrix += base_kernel(Gn, node_label, edge_label) return Kmatrix