OpenI
/
graphkit-learn

"""
@author: linlin
@references: 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 collections import Counter

import networkx as nx
import numpy as np


def untilnwalkkernel(*args, node_label = 'atom', edge_label = 'bond_type', labeled = True, n = 10):
    """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.
    labeled : boolean
        Whether the graphs are labeled. The default is True.
    n : integer
        Longest length of walks.

    Return
    ------
    Kmatrix : Numpy matrix
        Kernel matrix, each element of which is the path kernel up to d between 2 praphs.
    """
    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)))
    n = int(n)

    start_time = time.time()

    # 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 = node_label, edge_label = edge_label, labeled = 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] = _untilnwalkkernel_do(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 walk kernel up to %d of size %d built in %s seconds ---" % (n, len(Gn), run_time))

    return Kmatrix, run_time


def _untilnwalkkernel_do(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 = []
    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