graphkit-learn/pygraph/kernels/pathKernel.py

"""
@author: linlin
@references: Suard F, Rakotomamonjy A, Bensrhair A. Kernel on Bag of Paths For Measuring Similarity of Shapes. InESANN 2007 Apr 25 (pp. 355-360).
"""

import sys
import pathlib
sys.path.insert(0, "../")

import networkx as nx
import numpy as np
import time

from pygraph.kernels.deltaKernel import deltakernel

def pathkernel(*args, node_label = 'atom', edge_label = 'bond_type'):
    """Calculate mean average path 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.

    Return
    ------
    Kmatrix/kernel : Numpy matrix/float
        Kernel matrix, each element of which is the path kernel between 2 praphs. / Path kernel between 2 graphs.
    """
    some_graph = args[0][0] if len(args) == 1 else args[0] # only edge attributes of type int or float can be used as edge weight to calculate the shortest paths.
    some_weight = list(nx.get_edge_attributes(some_graph, edge_label).values())[0]
    weight = edge_label if isinstance(some_weight, float) or isinstance(some_weight, int) else None

    if len(args) == 1: # for a list of graphs
        Gn = args[0]
        Kmatrix = np.zeros((len(Gn), len(Gn)))

        start_time = time.time()

        splist = [ get_shortest_paths(Gn[i], weight) for i in range(0, len(Gn)) ]

        for i in range(0, len(Gn)):
            for j in range(i, len(Gn)):
                Kmatrix[i][j] = _pathkernel_do(Gn[i], Gn[j], splist[i], splist[j], node_label, edge_label)
                Kmatrix[j][i] = Kmatrix[i][j]

        run_time = time.time() - start_time
        print("\n --- mean average path kernel matrix of size %d built in %s seconds ---" % (len(Gn), run_time))

        return Kmatrix, run_time

    else: # for only 2 graphs
        start_time = time.time()

        splist = get_shortest_paths(args[0], weight)
        splist = get_shortest_paths(args[1], weight)

        kernel = _pathkernel_do(args[0], args[1], sp1, sp2, node_label, edge_label)

        run_time = time.time() - start_time
        print("\n --- mean average path kernel built in %s seconds ---" % (run_time))

        return kernel, run_time


def _pathkernel_do(G1, G2, sp1, sp2, node_label = 'atom', edge_label = 'bond_type'):
    """Calculate mean average path kernel between 2 graphs.

    Parameters
    ----------
    G1, G2 : NetworkX graphs
        2 graphs between which the kernel is calculated.
    sp1, sp2 : list of list
        List of shortest paths of 2 graphs, where each path is represented by a list of nodes.
    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.

    Return
    ------
    kernel : float
        Path Kernel between 2 graphs.
    """
    # calculate shortest paths for both graphs

    # calculate kernel
    kernel = 0
    for path1 in sp1:
        for path2 in sp2:
            if len(path1) == len(path2):
                kernel_path = (G1.node[path1[0]][node_label] == G2.node[path2[0]][node_label])
                if kernel_path:
                    for i in range(1, len(path1)):
                         # kernel = 1 if all corresponding nodes and edges in the 2 paths have same labels, otherwise 0
                        kernel_path *= (G1[path1[i - 1]][path1[i]][edge_label] == G2[path2[i - 1]][path2[i]][edge_label]) \
                            * (G1.node[path1[i]][node_label] == G2.node[path2[i]][node_label])
                        if kernel_path == 0:
                            break
                    kernel += kernel_path # add up kernels of all paths

    #                   kernel = 0
    # for path1 in sp1:
    #     for path2 in sp2:
    #         if len(path1) == len(path2):
    #             if (G1.node[path1[0]][node_label] == G2.node[path2[0]][node_label]):
    #                 for i in range(1, len(path1)):
    #                      # kernel = 1 if all corresponding nodes and edges in the 2 paths have same labels, otherwise 0
    #                 #     kernel_path *= (G1[path1[i - 1]][path1[i]][edge_label] == G2[path2[i - 1]][path2[i]][edge_label]) \
    #                 #         * (G1.node[path1[i]][node_label] == G2.node[path2[i]][node_label])
    #                 #     if kernel_path == 0:
    #                 #         break
    #                 # kernel += kernel_path # add up kernels of all paths
    #                     if (G1[path1[i - 1]][path1[i]][edge_label] != G2[path2[i - 1]][path2[i]][edge_label]) or \
    #                         (G1.node[path1[i]][node_label] != G2.node[path2[i]][node_label]):
    #                         break
    #                     else:
    #                         kernel += 1

    kernel = kernel / (len(sp1) * len(sp2)) # calculate mean average

    return kernel

def get_shortest_paths(G, weight):
    """Get all shortest paths of a graph.

    Parameters
    ----------
    G : NetworkX graphs
        The graphs whose paths are calculated.
    weight : string/None
        edge attribute used as weight to calculate the shortest path.

    Return
    ------
    sp : list of list
        List of shortest paths of the graph, where each path is represented by a list of nodes.
    """
    sp = []
    num_nodes = G.number_of_nodes()
    for node1 in range(num_nodes):
        for node2 in range(node1 + 1, num_nodes):
            sp.append(nx.shortest_path(G, node1, node2, weight = weight))
    return sp