OpenI
/
graphkit-learn

"""
@author: linlin
@references: Gaüzère B, Brun L, Villemin D. Two new graphs kernels in chemoinformatics. Pattern Recognition Letters. 2012 Nov 1;33(15):2038-47.
"""

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

from collections import Counter
from itertools import chain

import networkx as nx
import numpy as np


def treeletkernel(*args, node_label = 'atom', edge_label = 'bond_type', labeled = True):
    """Calculate treelet graph 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.
    labeled : boolean
        Whether the graphs are labeled. The default is True.

    Return
    ------
    Kmatrix/kernel : Numpy matrix/float
        Kernel matrix, each element of which is the treelet kernel between 2 praphs. / Treelet kernel between 2 graphs.
    """
    if len(args) == 1: # for a list of graphs
        Gn = args[0]
        Kmatrix = np.zeros((len(Gn), len(Gn)))

        start_time = time.time()

        # get all canonical keys of all graphs before calculating kernels to save time, but this may cost a lot of memory for large dataset.
        canonkeys = [ get_canonkeys(Gn[i], 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] = _treeletkernel_do(canonkeys[i], canonkeys[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 --- treelet 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()
                          
        canonkey1 = get_canonkeys(args[0], node_label = node_label, edge_label = edge_label, labeled = labeled)
        canonkey2 = get_canonkeys(args[1], node_label = node_label, edge_label = edge_label, labeled = labeled)
        
        kernel = _treeletkernel_do(canonkey1, canonkey2, node_label = node_label, edge_label = edge_label, labeled = labeled)
        
        run_time = time.time() - start_time
        print("\n --- treelet kernel built in %s seconds ---" % (run_time))

        return kernel, run_time


def _treeletkernel_do(canonkey1, canonkey2, node_label = 'atom', edge_label = 'bond_type', labeled = True):
    """Calculate treelet graph kernel between 2 graphs.
    
    Parameters
    ----------
    canonkey1, canonkey2 : list
        List of canonical keys in 2 graphs, where each key is represented by a string.
    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.
    """
    keys = set(canonkey1.keys()) & set(canonkey2.keys()) # find same canonical keys in both graphs
    vector1 = np.array([ (canonkey1[key] if (key in canonkey1.keys()) else 0) for key in keys ])
    vector2 = np.array([ (canonkey2[key] if (key in canonkey2.keys()) else 0) for key in keys ])        
    kernel = np.sum(np.exp(- np.square(vector1 - vector2) / 2))

    return kernel


def get_canonkeys(G, node_label = 'atom', edge_label = 'bond_type', labeled = True):
    """Generate canonical keys of all treelets in a graph.
    
    Parameters
    ----------
    G : NetworkX graphs
        The graph in which keys are generated.
    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
    ------
    canonkey/canonkey_l : dict
        For unlabeled graphs, canonkey is a dictionary which records amount of every tree pattern. For labeled graphs, canonkey_l is one which keeps track of amount of every treelet.
    """
    patterns = {} # a dictionary which consists of lists of patterns for all graphlet.
    canonkey = {} # canonical key, a dictionary which records amount of every tree pattern.

    ### structural analysis ###
    ### In this section, a list of patterns is generated for each graphlet, where every pattern is represented by nodes ordered by 
    ### Morgan's extended labeling.
    # linear patterns
    patterns['0'] = G.nodes()
    canonkey['0'] = nx.number_of_nodes(G)
    for i in range(1, 6): # for i in range(1, 6):
        patterns[str(i)] = find_all_paths(G, i)
        canonkey[str(i)] = len(patterns[str(i)])

    # n-star patterns
    patterns['3star'] = [ [node] + [neighbor for neighbor in G[node]] for node in G.nodes() if G.degree(node) == 3 ]
    patterns['4star'] = [ [node] + [neighbor for neighbor in G[node]] for node in G.nodes() if G.degree(node) == 4 ]
    patterns['5star'] = [ [node] + [neighbor for neighbor in G[node]] for node in G.nodes() if G.degree(node) == 5 ]        
    # n-star patterns
    canonkey['6'] = len(patterns['3star'])
    canonkey['8'] = len(patterns['4star'])
    canonkey['d'] = len(patterns['5star'])

    # pattern 7
    patterns['7'] = [] # the 1st line of Table 1 in Ref [1]
    for pattern in patterns['3star']:
        for i in range(1, len(pattern)): # for each neighbor of node 0
            if G.degree(pattern[i]) >= 2:
                pattern_t = pattern[:]
                pattern_t[i], pattern_t[3] = pattern_t[3], pattern_t[i] # set the node with degree >= 2 as the 4th node
                for neighborx in G[pattern[i]]:
                    if neighborx != pattern[0]:
                        new_pattern = pattern_t + [ neighborx ]
                        patterns['7'].append(new_pattern)
    canonkey['7'] = len(patterns['7'])

    # pattern 11
    patterns['11'] = [] # the 4th line of Table 1 in Ref [1]
    for pattern in patterns['4star']:
        for i in range(1, len(pattern)):
            if G.degree(pattern[i]) >= 2:
                pattern_t = pattern[:]
                pattern_t[i], pattern_t[4] = pattern_t[4], pattern_t[i]
                for neighborx in G[pattern[i]]:
                    if neighborx != pattern[0]:
                        new_pattern = pattern_t + [ neighborx ]
                        patterns['11'].append(new_pattern)
    canonkey['b'] = len(patterns['11'])

    # pattern 12
    patterns['12'] = [] # the 5th line of Table 1 in Ref [1]
    rootlist = [] # a list of root nodes, whose extended labels are 3
    for pattern in patterns['3star']:
        if pattern[0] not in rootlist: # prevent to count the same pattern twice from each of the two root nodes
            rootlist.append(pattern[0])
            for i in range(1, len(pattern)):
                if G.degree(pattern[i]) >= 3:
                    rootlist.append(pattern[i])
                    pattern_t = pattern[:]
                    pattern_t[i], pattern_t[3] = pattern_t[3], pattern_t[i]
                    for neighborx1 in G[pattern[i]]:
                        if neighborx1 != pattern[0]:
                            for neighborx2 in G[pattern[i]]:
                                if neighborx1 > neighborx2 and neighborx2 != pattern[0]:
                                    new_pattern = pattern_t + [neighborx1] + [neighborx2]
#                         new_patterns = [ pattern + [neighborx1] + [neighborx2] for neighborx1 in G[pattern[i]] if neighborx1 != pattern[0] for neighborx2 in G[pattern[i]] if (neighborx1 > neighborx2 and neighborx2 != pattern[0]) ]
                                    patterns['12'].append(new_pattern)
    canonkey['c'] = int(len(patterns['12']) / 2)

    # pattern 9
    patterns['9'] = [] # the 2nd line of Table 1 in Ref [1]
    for pattern in patterns['3star']:
        for pairs in [ [neighbor1, neighbor2] for neighbor1 in G[pattern[0]] if G.degree(neighbor1) >= 2 \
            for neighbor2 in G[pattern[0]] if G.degree(neighbor2) >= 2 if neighbor1 > neighbor2 ]:
            pattern_t = pattern[:]
            # move nodes with extended labels 4 to specific position to correspond to their children
            pattern_t[pattern_t.index(pairs[0])], pattern_t[2] = pattern_t[2], pattern_t[pattern_t.index(pairs[0])]
            pattern_t[pattern_t.index(pairs[1])], pattern_t[3] = pattern_t[3], pattern_t[pattern_t.index(pairs[1])]
            for neighborx1 in G[pairs[0]]:
                if neighborx1 != pattern[0]:
                    for neighborx2 in G[pairs[1]]:
                        if neighborx2 != pattern[0]:
                            new_pattern = pattern_t + [neighborx1] + [neighborx2]
                            patterns['9'].append(new_pattern)
    canonkey['9'] = len(patterns['9'])

    # pattern 10
    patterns['10'] = [] # the 3rd line of Table 1 in Ref [1]
    for pattern in patterns['3star']:        
        for i in range(1, len(pattern)):
            if G.degree(pattern[i]) >= 2:
                for neighborx in G[pattern[i]]:
                    if neighborx != pattern[0] and G.degree(neighborx) >= 2:
                        pattern_t = pattern[:]
                        pattern_t[i], pattern_t[3] = pattern_t[3], pattern_t[i]
                        new_patterns = [ pattern_t + [neighborx] + [neighborxx] for neighborxx in G[neighborx] if neighborxx != pattern[i] ]
                        patterns['10'].extend(new_patterns)
    canonkey['a'] = len(patterns['10'])

    ### labeling information ###
    ### In this section, a list of canonical keys is generated for every pattern obtained in the structural analysis
    ### section above, which is a string corresponding to a unique treelet. A dictionary is built to keep track of 
    ### the amount of every treelet.
    if labeled == True:
        canonkey_l = {} # canonical key, a dictionary which keeps track of amount of every treelet.

        # linear patterns
        canonkey_t = Counter(list(nx.get_node_attributes(G, node_label).values()))
        for key in canonkey_t:
            canonkey_l['0' + key] = canonkey_t[key]

        for i in range(1, 6): # for i in range(1, 6):
            treelet = []
            for pattern in patterns[str(i)]:
                canonlist = list(chain.from_iterable((G.node[node][node_label], \
                    G[node][pattern[idx+1]][edge_label]) for idx, node in enumerate(pattern[:-1])))
                canonlist.append(G.node[pattern[-1]][node_label])
                canonkey_t = ''.join(canonlist)
                canonkey_t = canonkey_t if canonkey_t < canonkey_t[::-1] else canonkey_t[::-1]
                treelet.append(str(i) + canonkey_t)
            canonkey_l.update(Counter(treelet))

        # n-star patterns
        for i in range(3, 6):
            treelet = []
            for pattern in patterns[str(i) + 'star']:
                canonlist = [ G.node[leaf][node_label] + G[leaf][pattern[0]][edge_label] for leaf in pattern[1:] ]
                canonlist.sort()
                canonkey_t = ('d' if i == 5 else str(i * 2)) + G.node[pattern[0]][node_label] + ''.join(canonlist)
                treelet.append(canonkey_t)
            canonkey_l.update(Counter(treelet))

        # pattern 7
        treelet = []
        for pattern in patterns['7']:
            canonlist = [ G.node[leaf][node_label] + G[leaf][pattern[0]][edge_label] for leaf in pattern[1:3] ]
            canonlist.sort()
            canonkey_t = '7' + G.node[pattern[0]][node_label] + ''.join(canonlist) \
                + G.node[pattern[3]][node_label] + G[pattern[3]][pattern[0]][edge_label] \
                 + G.node[pattern[4]][node_label] + G[pattern[4]][pattern[3]][edge_label]
            treelet.append(canonkey_t)
        canonkey_l.update(Counter(treelet))

        # pattern 11
        treelet = []
        for pattern in patterns['11']:
            canonlist = [ G.node[leaf][node_label] + G[leaf][pattern[0]][edge_label] for leaf in pattern[1:4] ]
            canonlist.sort()
            canonkey_t = 'b' + G.node[pattern[0]][node_label] + ''.join(canonlist) \
                + G.node[pattern[4]][node_label] + G[pattern[4]][pattern[0]][edge_label] \
                 + G.node[pattern[5]][node_label] + G[pattern[5]][pattern[4]][edge_label]
            treelet.append(canonkey_t)
        canonkey_l.update(Counter(treelet))

        # pattern 10
        treelet = []
        for pattern in patterns['10']:
            canonkey4 = G.node[pattern[5]][node_label] + G[pattern[5]][pattern[4]][edge_label]
            canonlist = [ G.node[leaf][node_label] + G[leaf][pattern[0]][edge_label] for leaf in pattern[1:3] ]
            canonlist.sort()
            canonkey0 = ''.join(canonlist)
            canonkey_t = 'a' + G.node[pattern[3]][node_label] \
                + G.node[pattern[4]][node_label] + G[pattern[4]][pattern[3]][edge_label] \
                + G.node[pattern[0]][node_label] + G[pattern[0]][pattern[3]][edge_label] \
                + canonkey4 + canonkey0
            treelet.append(canonkey_t)
        canonkey_l.update(Counter(treelet))

        # pattern 12
        treelet = []
        for pattern in patterns['12']:
            canonlist0 = [ G.node[leaf][node_label] + G[leaf][pattern[0]][edge_label] for leaf in pattern[1:3] ]
            canonlist0.sort()
            canonlist3 = [ G.node[leaf][node_label] + G[leaf][pattern[3]][edge_label] for leaf in pattern[4:6] ]
            canonlist3.sort()
            
            # 2 possible key can be generated from 2 nodes with extended label 3, select the one with lower lexicographic order.
            canonkey_t1 = 'c' + G.node[pattern[0]][node_label] \
                + ''.join(canonlist0) \
                + G.node[pattern[3]][node_label] + G[pattern[3]][pattern[0]][edge_label] \
                + ''.join(canonlist3)

            canonkey_t2 = 'c' + G.node[pattern[3]][node_label] \
                + ''.join(canonlist3) \
                + G.node[pattern[0]][node_label] + G[pattern[0]][pattern[3]][edge_label] \
                + ''.join(canonlist0)

            treelet.append(canonkey_t1 if canonkey_t1 < canonkey_t2 else canonkey_t2)
        canonkey_l.update(Counter(treelet))

        # pattern 9
        treelet = []
        for pattern in patterns['9']:
            canonkey2 = G.node[pattern[4]][node_label] + G[pattern[4]][pattern[2]][edge_label]
            canonkey3 = G.node[pattern[5]][node_label] + G[pattern[5]][pattern[3]][edge_label]
            prekey2 = G.node[pattern[2]][node_label] + G[pattern[2]][pattern[0]][edge_label]
            prekey3 = G.node[pattern[3]][node_label] + G[pattern[3]][pattern[0]][edge_label]
            if prekey2 + canonkey2 < prekey3 + canonkey3:
                canonkey_t = G.node[pattern[1]][node_label] + G[pattern[1]][pattern[0]][edge_label] \
                    + prekey2 + prekey3 + canonkey2 + canonkey3
            else:
                canonkey_t = G.node[pattern[1]][node_label] + G[pattern[1]][pattern[0]][edge_label] \
                    + prekey3 + prekey2 + canonkey3 + canonkey2
            treelet.append('9' + G.node[pattern[0]][node_label] + canonkey_t)
        canonkey_l.update(Counter(treelet))

        return canonkey_l

    return canonkey
    

def find_paths(G, source_node, length):
    """Find all paths 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 paths are searched.
    source_node : integer
        The number of the node from where all paths start.
    length : integer
        The length of paths.
        
    Return
    ------
    path : list of list
        List of paths retrieved, where each path is represented by a list of nodes.
    """
    if length == 0:
        return [[source_node]]
    path = [ [source_node] + path for neighbor in G[source_node] \
        for path in find_paths(G, neighbor, length - 1) if source_node not in path ]
    return path


def find_all_paths(G, length):
    """Find all paths with a certain length in a graph. A recursive depth first search is applied.
    
    Parameters
    ----------
    G : NetworkX graphs
        The graph in which paths are searched.
    length : integer
        The length of paths.
        
    Return
    ------
    path : list of list
        List of paths retrieved, where each path is represented by a list of nodes.
    """
    all_paths = []
    for node in G:
        all_paths.extend(find_paths(G, node, length))
    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))