""" @author: linlin @references: [1] Thomas Gärtner, Peter Flach, and Stefan Wrobel. On graph kernels: Hardness results and efficient alternatives. Learning Theory and Kernel Machines, pages 129–143, 2003. """ import sys import pathlib sys.path.insert(0, "../") import time from tqdm import tqdm from collections import Counter from itertools import product import networkx as nx import numpy as np from pygraph.utils.utils import direct_product from pygraph.utils.graphdataset import get_dataset_attributes def commonwalkkernel(*args, node_label='atom', edge_label='bond_type', n=None, weight=1, compute_method=None): """Calculate common walk graph kernels up to depth d 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. n : integer Longest length of walks. weight: integer Weight coefficient of different lengths of walks, which represents beta in 'exp' method and gamma in 'geo'. compute_method : string Method used to compute walk kernel. The Following choices are available: 'exp' : exponential serial method applied on the direct product graph, as shown in reference [1]. The time complexity is O(n^6) for graphs with n vertices. 'geo' : geometric serial method applied on the direct product graph, as shown in reference [1]. The time complexity is O(n^6) for graphs with n vertices. 'brute' : brute force, simply search for all walks and compare them. Return ------ Kmatrix : Numpy matrix Kernel matrix, each element of which is the path kernel up to d between 2 graphs. """ compute_method = compute_method.lower() # arrange all graphs in a list Gn = args[0] if len(args) == 1 else [args[0], args[1]] Kmatrix = np.zeros((len(Gn), len(Gn))) ds_attrs = get_dataset_attributes( Gn, attr_names=['node_labeled', 'edge_labeled', 'is_directed'], node_label=node_label, edge_label=edge_label) if not ds_attrs['node_labeled']: for G in Gn: nx.set_node_attributes(G, '0', 'atom') if not ds_attrs['edge_labeled']: for G in Gn: nx.set_edge_attributes(G, '0', 'bond_type') if not ds_attrs['is_directed']: Gn = [G.to_directed() for G in Gn] start_time = time.time() # direct product graph method - exponential if compute_method == 'exp': pbar = tqdm( total=(1 + len(Gn)) * len(Gn) / 2, desc='calculating kernels', file=sys.stdout) for i in range(0, len(Gn)): for j in range(i, len(Gn)): Kmatrix[i][j] = _commonwalkkernel_exp(Gn[i], Gn[j], node_label, edge_label, weight) Kmatrix[j][i] = Kmatrix[i][j] pbar.update(1) # direct product graph method - geometric if compute_method == 'geo': pbar = tqdm( total=(1 + len(Gn)) * len(Gn) / 2, desc='calculating kernels', file=sys.stdout) for i in range(0, len(Gn)): for j in range(i, len(Gn)): Kmatrix[i][j] = _commonwalkkernel_geo(Gn[i], Gn[j], node_label, edge_label, weight) Kmatrix[j][i] = Kmatrix[i][j] pbar.update(1) # search all paths use brute force. elif compute_method == 'brute': n = int(n) # get all paths of all graphs before calculating kernels to save time, but this may cost a lot of memory for large dataset. all_walks = [ find_all_walks_until_length(Gn[i], n, node_label, edge_label, labeled) for i in range(0, len(Gn)) ] for i in range(0, len(Gn)): for j in range(i, len(Gn)): Kmatrix[i][j] = _commonwalkkernel_brute( all_walks[i], all_walks[j], node_label=node_label, edge_label=edge_label, labeled=labeled) Kmatrix[j][i] = Kmatrix[i][j] run_time = time.time() - start_time print( "\n --- kernel matrix of common walk kernel of size %d built in %s seconds ---" % (len(Gn), run_time)) return Kmatrix, run_time def _commonwalkkernel_exp(G1, G2, node_label, edge_label, beta): """Calculate walk graph kernels up to n between 2 graphs using exponential series. Parameters ---------- G1, G2 : NetworkX graph Graphs between which the kernel is calculated. node_label : string Node attribute used as label. edge_label : string Edge attribute used as label. beta: integer Weight. Return ------ kernel : float Treelet Kernel between 2 graphs. """ # get tensor product / direct product gp = direct_product(G1, G2, node_label, edge_label) A = nx.adjacency_matrix(gp).todense() # print(A) # from matplotlib import pyplot as plt # nx.draw_networkx(G1) # plt.show() # nx.draw_networkx(G2) # plt.show() # nx.draw_networkx(gp) # plt.show() # print(G1.nodes(data=True)) # print(G2.nodes(data=True)) # print(gp.nodes(data=True)) # print(gp.edges(data=True)) ew, ev = np.linalg.eig(A) # print('ew: ', ew) # print(ev) # T = np.matrix(ev) # print('T: ', T) # T = ev.I D = np.zeros((len(ew), len(ew))) for i in range(len(ew)): D[i][i] = np.exp(beta * ew[i]) # print('D: ', D) # print('hshs: ', T.I * D * T) # print(np.exp(-2)) # print(D) # print(np.exp(weight * D)) # print(ev) # print(np.linalg.inv(ev)) exp_D = ev * D * ev.T # print(exp_D) # print(np.exp(weight * A)) # print('-------') return exp_D.sum() def _commonwalkkernel_geo(G1, G2, node_label, edge_label, gamma): """Calculate common walk graph kernels up to n between 2 graphs using geometric series. Parameters ---------- G1, G2 : NetworkX graph Graphs between which the kernel is calculated. node_label : string Node attribute used as label. edge_label : string Edge attribute used as label. gamma: integer Weight. Return ------ kernel : float Treelet Kernel between 2 graphs. """ # get tensor product / direct product gp = direct_product(G1, G2, node_label, edge_label) A = nx.adjacency_matrix(gp).todense() mat = np.identity(len(A)) - gamma * A try: return mat.I.sum() except np.linalg.LinAlgError: return np.nan def _commonwalkkernel_brute(walks1, walks2, node_label='atom', edge_label='bond_type', labeled=True): """Calculate walk graph kernels up to n between 2 graphs. Parameters ---------- walks1, walks2 : list List of walks in 2 graphs, where for unlabeled graphs, each walk is represented by a list of nodes; while for labeled graphs, each walk is represented by a string consists of labels of nodes and edges on that walk. 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. labeled : boolean Whether the graphs are labeled. The default is True. Return ------ kernel : float Treelet Kernel between 2 graphs. """ counts_walks1 = dict(Counter(walks1)) counts_walks2 = dict(Counter(walks2)) all_walks = list(set(walks1 + walks2)) vector1 = [(counts_walks1[walk] if walk in walks1 else 0) for walk in all_walks] vector2 = [(counts_walks2[walk] if walk in walks2 else 0) for walk in all_walks] kernel = np.dot(vector1, vector2) return kernel # this method find walks repetively, it could be faster. def find_all_walks_until_length(G, length, node_label='atom', edge_label='bond_type', labeled=True): """Find all walks with a certain maximum length in a graph. A recursive depth first search is applied. Parameters ---------- G : NetworkX graphs The graph in which walks are searched. length : integer The maximum length of walks. 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. labeled : boolean Whether the graphs are labeled. The default is True. Return ------ walk : list List of walks retrieved, where for unlabeled graphs, each walk is represented by a list of nodes; while for labeled graphs, each walk is represented by a string consists of labels of nodes and edges on that walk. """ all_walks = [] # @todo: in this way, the time complexity is close to N(d^n+d^(n+1)+...+1), which could be optimized to O(Nd^n) for i in range(0, length + 1): new_walks = find_all_walks(G, i) if new_walks == []: break all_walks.extend(new_walks) if labeled == True: # convert paths to strings walk_strs = [] for walk in all_walks: strlist = [ G.node[node][node_label] + G[node][walk[walk.index(node) + 1]][edge_label] for node in walk[:-1] ] walk_strs.append(''.join(strlist) + G.node[walk[-1]][node_label]) return walk_strs return all_walks def find_walks(G, source_node, length): """Find all walks with a certain length those start from a source node. A recursive depth first search is applied. Parameters ---------- G : NetworkX graphs The graph in which walks are searched. source_node : integer The number of the node from where all walks start. length : integer The length of walks. Return ------ walk : list of list List of walks retrieved, where each walk is represented by a list of nodes. """ return [[source_node]] if length == 0 else \ [ [source_node] + walk for neighbor in G[source_node] \ for walk in find_walks(G, neighbor, length - 1) ] def find_all_walks(G, length): """Find all walks with a certain length in a graph. A recursive depth first search is applied. Parameters ---------- G : NetworkX graphs The graph in which walks are searched. length : integer The length of walks. Return ------ walk : list of list List of walks retrieved, where each walk is represented by a list of nodes. """ all_walks = [] for node in G: all_walks.extend(find_walks(G, node, length)) ### The following process is not carried out according to the original article # all_paths_r = [ path[::-1] for path in all_paths ] # # For each path, two presentation are retrieved from its two extremities. Remove one of them. # for idx, path in enumerate(all_paths[:-1]): # for path2 in all_paths_r[idx+1::]: # if path == path2: # all_paths[idx] = [] # break # return list(filter(lambda a: a != [], all_paths)) return all_walks