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New translations randomWalkKernel.py (Chinese Simplified)

l10n_v0.2.x
linlin 5 years ago
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      lang/zh/gklearn/kernels/randomWalkKernel.py

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"""
@author: linlin

@references:

[1] S Vichy N Vishwanathan, Nicol N Schraudolph, Risi Kondor, and Karsten M Borgwardt. Graph kernels. Journal of Machine Learning Research, 11(Apr):1201–1242, 2010.
"""

import time
from functools import partial
from tqdm import tqdm
import sys

import networkx as nx
import numpy as np
from scipy.sparse import identity, kron
from scipy.sparse.linalg import cg
from scipy.optimize import fixed_point

from gklearn.utils.graphdataset import get_dataset_attributes
from gklearn.utils.parallel import parallel_gm

def randomwalkkernel(*args,
# params for all method.
compute_method=None,
weight=1,
p=None,
q=None,
edge_weight=None,
# params for conjugate and fp method.
node_kernels=None,
edge_kernels=None,
node_label='atom',
edge_label='bond_type',
# params for spectral method.
sub_kernel=None,
n_jobs=None,
chunksize=None,
verbose=True):
"""Calculate random walk graph kernels.

Parameters
----------
Gn : List of NetworkX graph
List of graphs between which the kernels are calculated.
G1, G2 : NetworkX graphs
Two graphs between which the kernel is calculated.

compute_method : string
Method used to compute kernel. The Following choices are
available:

'sylvester' - Sylvester equation method.

'conjugate' - conjugate gradient method.

'fp' - fixed-point iterations.

'spectral' - spectral decomposition.

weight : float
A constant weight set for random walks of length h.

p : None
Initial probability distribution on the unlabeled direct product graph
of two graphs. It is set to be uniform over all vertices in the direct
product graph.

q : None
Stopping probability distribution on the unlabeled direct product graph
of two graphs. It is set to be uniform over all vertices in the direct
product graph.

edge_weight : float

Edge attribute name corresponding to the edge weight.
node_kernels: dict
A dictionary of kernel functions for nodes, including 3 items: 'symb'
for symbolic node labels, 'nsymb' for non-symbolic node labels, 'mix'
for both labels. The first 2 functions take two node labels as
parameters, and the 'mix' function takes 4 parameters, a symbolic and a
non-symbolic label for each the two nodes. Each label is in form of 2-D
dimension array (n_samples, n_features). Each function returns a number
as the kernel value. Ignored when nodes are unlabeled. This argument
is designated to conjugate gradient method and fixed-point iterations.

edge_kernels: dict
A dictionary of kernel functions for edges, including 3 items: 'symb'
for symbolic edge labels, 'nsymb' for non-symbolic edge labels, 'mix'
for both labels. The first 2 functions take two edge labels as
parameters, and the 'mix' function takes 4 parameters, a symbolic and a
non-symbolic label for each the two edges. Each label is in form of 2-D
dimension array (n_samples, n_features). Each function returns a number
as the kernel value. Ignored when edges are unlabeled. This argument
is designated to conjugate gradient method and fixed-point iterations.

node_label: string
Node attribute used as label. The default node label is atom. This
argument is designated to conjugate gradient method and fixed-point
iterations.

edge_label : string
Edge attribute used as label. The default edge label is bond_type. This
argument is designated to conjugate gradient method and fixed-point
iterations.
sub_kernel: string
Method used to compute walk kernel. The Following choices are
available:
'exp' : method based on exponential serials.
'geo' : method based on geometric serials.
n_jobs: int
Number of jobs for parallelization.

Return
------
Kmatrix : Numpy matrix
Kernel matrix, each element of which is the path kernel up to d between 2 praphs.
"""
compute_method = compute_method.lower()
Gn = args[0] if len(args) == 1 else [args[0], args[1]]
Gn = [g.copy() for g in Gn]

eweight = None
if edge_weight == None:
if verbose:
print('\n None edge weight specified. Set all weight to 1.\n')
else:
try:
some_weight = list(
nx.get_edge_attributes(Gn[0], edge_weight).values())[0]
if isinstance(some_weight, float) or isinstance(some_weight, int):
eweight = edge_weight
else:
if verbose:
print('\n Edge weight with name %s is not float or integer. Set all weight to 1.\n'
% edge_weight)
except:
if verbose:
print('\n Edge weight with name "%s" is not found in the edge attributes. Set all weight to 1.\n'
% edge_weight)

ds_attrs = get_dataset_attributes(
Gn,
attr_names=['node_labeled', 'node_attr_dim', 'edge_labeled',
'edge_attr_dim', 'is_directed'],
node_label=node_label,
edge_label=edge_label)
# remove graphs with no edges, as no walk can be found in their structures,
# so the weight matrix between such a graph and itself might be zero.
len_gn = len(Gn)
Gn = [(idx, G) for idx, G in enumerate(Gn) if nx.number_of_edges(G) != 0]
idx = [G[0] for G in Gn]
Gn = [G[1] for G in Gn]
if len(Gn) != len_gn:
if verbose:
print('\n %d graphs are removed as they don\'t contain edges.\n' %
(len_gn - len(Gn)))

start_time = time.time()
# # get vertex and edge concatenated labels for each graph
# label_list, d = getLabels(Gn, node_label, edge_label, ds_attrs['is_directed'])
# gmf = filterGramMatrix(A_wave_list[0], label_list[0], ('C', '0', 'O'), ds_attrs['is_directed'])

if compute_method == 'sylvester':
if verbose:
import warnings
warnings.warn('All labels are ignored.')
Kmatrix = _sylvester_equation(Gn, weight, p, q, eweight, n_jobs, chunksize, verbose=verbose)

elif compute_method == 'conjugate':
Kmatrix = _conjugate_gradient(Gn, weight, p, q, ds_attrs, node_kernels,
edge_kernels, node_label, edge_label,
eweight, n_jobs, chunksize, verbose=verbose)
elif compute_method == 'fp':
Kmatrix = _fixed_point(Gn, weight, p, q, ds_attrs, node_kernels,
edge_kernels, node_label, edge_label,
eweight, n_jobs, chunksize, verbose=verbose)

elif compute_method == 'spectral':
if verbose:
import warnings
warnings.warn('All labels are ignored. Only works for undirected graphs.')
Kmatrix = _spectral_decomposition(Gn, weight, p, q, sub_kernel,
eweight, n_jobs, chunksize, verbose=verbose)

elif compute_method == 'kron':
pass
for i in range(0, len(Gn)):
for j in range(i, len(Gn)):
Kmatrix[i][j] = _randomwalkkernel_kron(Gn[i], Gn[j],
node_label, edge_label)
Kmatrix[j][i] = Kmatrix[i][j]
else:
raise Exception(
'compute method name incorrect. Available methods: "sylvester", "conjugate", "fp", "spectral" and "kron".'
)

run_time = time.time() - start_time
if verbose:
print("\n --- kernel matrix of random walk kernel of size %d built in %s seconds ---"
% (len(Gn), run_time))

return Kmatrix, run_time, idx


###############################################################################
def _sylvester_equation(Gn, lmda, p, q, eweight, n_jobs, chunksize, verbose=True):
"""Calculate walk graph kernels up to n between 2 graphs using Sylvester method.

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.

Return
------
kernel : float
Kernel between 2 graphs.
"""
Kmatrix = np.zeros((len(Gn), len(Gn)))

if q == None:
# don't normalize adjacency matrices if q is a uniform vector. Note
# A_wave_list actually contains the transposes of the adjacency matrices.
A_wave_list = [
nx.adjacency_matrix(G, eweight).todense().transpose() for G in
(tqdm(Gn, desc='compute adjacency matrices', file=sys.stdout) if
verbose else Gn)
]
# # normalized adjacency matrices
# A_wave_list = []
# for G in tqdm(Gn, desc='compute adjacency matrices', file=sys.stdout):
# A_tilde = nx.adjacency_matrix(G, eweight).todense().transpose()
# norm = A_tilde.sum(axis=0)
# norm[norm == 0] = 1
# A_wave_list.append(A_tilde / norm)
if p == None: # p is uniform distribution as default.
def init_worker(Awl_toshare):
global G_Awl
G_Awl = Awl_toshare
do_partial = partial(wrapper_se_do, lmda)
parallel_gm(do_partial, Kmatrix, Gn, init_worker=init_worker,
glbv=(A_wave_list,), n_jobs=n_jobs, chunksize=chunksize, verbose=verbose)
# 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)):
# S = lmda * A_wave_list[j]
# T_t = A_wave_list[i]
# # use uniform distribution if there is no prior knowledge.
# nb_pd = len(A_wave_list[i]) * len(A_wave_list[j])
# p_times_uni = 1 / nb_pd
# M0 = np.full((len(A_wave_list[j]), len(A_wave_list[i])), p_times_uni)
# X = dlyap(S, T_t, M0)
# X = np.reshape(X, (-1, 1), order='F')
# # use uniform distribution if there is no prior knowledge.
# q_times = np.full((1, nb_pd), p_times_uni)
# Kmatrix[i][j] = np.dot(q_times, X)
# Kmatrix[j][i] = Kmatrix[i][j]
# pbar.update(1)

return Kmatrix


def wrapper_se_do(lmda, itr):
i = itr[0]
j = itr[1]
return i, j, _se_do(G_Awl[i], G_Awl[j], lmda)


def _se_do(A_wave1, A_wave2, lmda):
from control import dlyap
S = lmda * A_wave2
T_t = A_wave1
# use uniform distribution if there is no prior knowledge.
nb_pd = len(A_wave1) * len(A_wave2)
p_times_uni = 1 / nb_pd
M0 = np.full((len(A_wave2), len(A_wave1)), p_times_uni)
X = dlyap(S, T_t, M0)
X = np.reshape(X, (-1, 1), order='F')
# use uniform distribution if there is no prior knowledge.
q_times = np.full((1, nb_pd), p_times_uni)
return np.dot(q_times, X)


###############################################################################
def _conjugate_gradient(Gn, lmda, p, q, ds_attrs, node_kernels, edge_kernels,
node_label, edge_label, eweight, n_jobs, chunksize, verbose=True):
"""Calculate walk graph kernels up to n between 2 graphs using conjugate method.

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.

Return
------
kernel : float
Kernel between 2 graphs.
"""
Kmatrix = np.zeros((len(Gn), len(Gn)))
# if not ds_attrs['node_labeled'] and ds_attrs['node_attr_dim'] < 1 and \
# not ds_attrs['edge_labeled'] and ds_attrs['edge_attr_dim'] < 1:
# # this is faster from unlabeled graphs. @todo: why?
# if q == None:
# # don't normalize adjacency matrices if q is a uniform vector. Note
# # A_wave_list actually contains the transposes of the adjacency matrices.
# A_wave_list = [
# nx.adjacency_matrix(G, eweight).todense().transpose() for G in
# tqdm(Gn, desc='compute adjacency matrices', file=sys.stdout)
# ]
# if p == None: # p is uniform distribution as default.
# def init_worker(Awl_toshare):
# global G_Awl
# G_Awl = Awl_toshare
# do_partial = partial(wrapper_cg_unlabled_do, lmda)
# parallel_gm(do_partial, Kmatrix, Gn, init_worker=init_worker,
# glbv=(A_wave_list,), n_jobs=n_jobs)
# else:
# reindex nodes using consecutive integers for convenience of kernel calculation.
Gn = [nx.convert_node_labels_to_integers(
g, first_label=0, label_attribute='label_orignal') for g in (tqdm(
Gn, desc='reindex vertices', file=sys.stdout) if verbose else Gn)]
if p == None and q == None: # p and q are uniform distributions as default.
def init_worker(gn_toshare):
global G_gn
G_gn = gn_toshare
do_partial = partial(wrapper_cg_labled_do, ds_attrs, node_kernels,
node_label, edge_kernels, edge_label, lmda)
parallel_gm(do_partial, Kmatrix, Gn, init_worker=init_worker,
glbv=(Gn,), n_jobs=n_jobs, chunksize=chunksize, verbose=verbose)
# 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)):
# result = _cg_labled_do(Gn[i], Gn[j], ds_attrs, node_kernels,
# node_label, edge_kernels, edge_label, lmda)
# Kmatrix[i][j] = result
# Kmatrix[j][i] = Kmatrix[i][j]
# pbar.update(1)
return Kmatrix


def wrapper_cg_unlabled_do(lmda, itr):
i = itr[0]
j = itr[1]
return i, j, _cg_unlabled_do(G_Awl[i], G_Awl[j], lmda)


def _cg_unlabled_do(A_wave1, A_wave2, lmda):
nb_pd = len(A_wave1) * len(A_wave2)
p_times_uni = 1 / nb_pd
w_times = kron(A_wave1, A_wave2).todense()
A = identity(w_times.shape[0]) - w_times * lmda
b = np.full((nb_pd, 1), p_times_uni)
x, _ = cg(A, b)
# use uniform distribution if there is no prior knowledge.
q_times = np.full((1, nb_pd), p_times_uni)
return np.dot(q_times, x)


def wrapper_cg_labled_do(ds_attrs, node_kernels, node_label, edge_kernels,
edge_label, lmda, itr):
i = itr[0]
j = itr[1]
return i, j, _cg_labled_do(G_gn[i], G_gn[j], ds_attrs, node_kernels,
node_label, edge_kernels, edge_label, lmda)


def _cg_labled_do(g1, g2, ds_attrs, node_kernels, node_label,
edge_kernels, edge_label, lmda):
# Frist, compute kernels between all pairs of nodes, method borrowed
# from FCSP. It is faster than directly computing all edge kernels
# when $d_1d_2>2$, where $d_1$ and $d_2$ are vertex degrees of the
# graphs compared, which is the most case we went though. For very
# sparse graphs, this would be slow.
vk_dict = computeVK(g1, g2, ds_attrs, node_kernels, node_label)
# Compute weight matrix of the direct product graph.
w_times, w_dim = computeW(g1, g2, vk_dict, ds_attrs,
edge_kernels, edge_label)
# use uniform distribution if there is no prior knowledge.
p_times_uni = 1 / w_dim
A = identity(w_times.shape[0]) - w_times * lmda
b = np.full((w_dim, 1), p_times_uni)
x, _ = cg(A, b)
# use uniform distribution if there is no prior knowledge.
q_times = np.full((1, w_dim), p_times_uni)
return np.dot(q_times, x)


###############################################################################
def _fixed_point(Gn, lmda, p, q, ds_attrs, node_kernels, edge_kernels,
node_label, edge_label, eweight, n_jobs, chunksize, verbose=True):
"""Calculate walk graph kernels up to n between 2 graphs using Fixed-Point method.

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.

Return
------
kernel : float
Kernel between 2 graphs.
"""

Kmatrix = np.zeros((len(Gn), len(Gn)))
# if not ds_attrs['node_labeled'] and ds_attrs['node_attr_dim'] < 1 and \
# not ds_attrs['edge_labeled'] and ds_attrs['edge_attr_dim'] > 1:
# # this is faster from unlabeled graphs. @todo: why?
# if q == None:
# # don't normalize adjacency matrices if q is a uniform vector. Note
# # A_wave_list actually contains the transposes of the adjacency matrices.
# A_wave_list = [
# nx.adjacency_matrix(G, eweight).todense().transpose() for G in
# tqdm(Gn, desc='compute adjacency matrices', file=sys.stdout)
# ]
# if p == None: # p is uniform distribution as default.
# 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)):
# # use uniform distribution if there is no prior knowledge.
# nb_pd = len(A_wave_list[i]) * len(A_wave_list[j])
# p_times_uni = 1 / nb_pd
# w_times = kron(A_wave_list[i], A_wave_list[j]).todense()
# p_times = np.full((nb_pd, 1), p_times_uni)
# x = fixed_point(func_fp, p_times, args=(p_times, lmda, w_times))
# # use uniform distribution if there is no prior knowledge.
# q_times = np.full((1, nb_pd), p_times_uni)
# Kmatrix[i][j] = np.dot(q_times, x)
# Kmatrix[j][i] = Kmatrix[i][j]
# pbar.update(1)
# else:
# reindex nodes using consecutive integers for convenience of kernel calculation.
Gn = [nx.convert_node_labels_to_integers(
g, first_label=0, label_attribute='label_orignal') for g in (tqdm(
Gn, desc='reindex vertices', file=sys.stdout) if verbose else Gn)]
if p == None and q == None: # p and q are uniform distributions as default.
def init_worker(gn_toshare):
global G_gn
G_gn = gn_toshare
do_partial = partial(wrapper_fp_labled_do, ds_attrs, node_kernels,
node_label, edge_kernels, edge_label, lmda)
parallel_gm(do_partial, Kmatrix, Gn, init_worker=init_worker,
glbv=(Gn,), n_jobs=n_jobs, chunksize=chunksize, verbose=verbose)
return Kmatrix


def wrapper_fp_labled_do(ds_attrs, node_kernels, node_label, edge_kernels,
edge_label, lmda, itr):
i = itr[0]
j = itr[1]
return i, j, _fp_labled_do(G_gn[i], G_gn[j], ds_attrs, node_kernels,
node_label, edge_kernels, edge_label, lmda)


def _fp_labled_do(g1, g2, ds_attrs, node_kernels, node_label,
edge_kernels, edge_label, lmda):
# Frist, compute kernels between all pairs of nodes, method borrowed
# from FCSP. It is faster than directly computing all edge kernels
# when $d_1d_2>2$, where $d_1$ and $d_2$ are vertex degrees of the
# graphs compared, which is the most case we went though. For very
# sparse graphs, this would be slow.
vk_dict = computeVK(g1, g2, ds_attrs, node_kernels, node_label)
# Compute weight matrix of the direct product graph.
w_times, w_dim = computeW(g1, g2, vk_dict, ds_attrs,
edge_kernels, edge_label)
# use uniform distribution if there is no prior knowledge.
p_times_uni = 1 / w_dim
p_times = np.full((w_dim, 1), p_times_uni)
x = fixed_point(func_fp, p_times, args=(p_times, lmda, w_times),
xtol=1e-06, maxiter=1000)
# use uniform distribution if there is no prior knowledge.
q_times = np.full((1, w_dim), p_times_uni)
return np.dot(q_times, x)


def func_fp(x, p_times, lmda, w_times):
haha = w_times * x
haha = lmda * haha
haha = p_times + haha
return p_times + lmda * np.dot(w_times, x)


###############################################################################
def _spectral_decomposition(Gn, weight, p, q, sub_kernel, eweight, n_jobs, chunksize, verbose=True):
"""Calculate walk graph kernels up to n between 2 unlabeled graphs using
spectral decomposition method. Labels will be ignored.

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.

Return
------
kernel : float
Kernel between 2 graphs.
"""
Kmatrix = np.zeros((len(Gn), len(Gn)))

if q == None:
# precompute the spectral decomposition of each graph.
P_list = []
D_list = []
for G in (tqdm(Gn, desc='spectral decompose', file=sys.stdout) if
verbose else Gn):
# don't normalize adjacency matrices if q is a uniform vector. Note
# A actually is the transpose of the adjacency matrix.
A = nx.adjacency_matrix(G, eweight).todense().transpose()
ew, ev = np.linalg.eig(A)
D_list.append(ew)
P_list.append(ev)
# P_inv_list = [p.T for p in P_list] # @todo: also works for directed graphs?

if p == None: # p is uniform distribution as default.
q_T_list = [np.full((1, nx.number_of_nodes(G)), 1 / nx.number_of_nodes(G)) for G in Gn]
# q_T_list = [q.T for q in q_list]
def init_worker(q_T_toshare, P_toshare, D_toshare):
global G_q_T, G_P, G_D
G_q_T = q_T_toshare
G_P = P_toshare
G_D = D_toshare
do_partial = partial(wrapper_sd_do, weight, sub_kernel)
parallel_gm(do_partial, Kmatrix, Gn, init_worker=init_worker,
glbv=(q_T_list, P_list, D_list), n_jobs=n_jobs,
chunksize=chunksize, verbose=verbose)
# 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)):
# result = _sd_do(q_T_list[i], q_T_list[j], P_list[i], P_list[j],
# D_list[i], D_list[j], weight, sub_kernel)
# Kmatrix[i][j] = result
# Kmatrix[j][i] = Kmatrix[i][j]
# pbar.update(1)
return Kmatrix


def wrapper_sd_do(weight, sub_kernel, itr):
i = itr[0]
j = itr[1]
return i, j, _sd_do(G_q_T[i], G_q_T[j], G_P[i], G_P[j], G_D[i], G_D[j],
weight, sub_kernel)


def _sd_do(q_T1, q_T2, P1, P2, D1, D2, weight, sub_kernel):
# use uniform distribution if there is no prior knowledge.
kl = kron(np.dot(q_T1, P1), np.dot(q_T2, P2)).todense()
# @todo: this is not be needed when p = q (kr = kl.T) for undirected graphs
# kr = kron(np.dot(P_inv_list[i], q_list[i]), np.dot(P_inv_list[j], q_list[j])).todense()
if sub_kernel == 'exp':
D_diag = np.array([d1 * d2 for d1 in D1 for d2 in D2])
kmiddle = np.diag(np.exp(weight * D_diag))
elif sub_kernel == 'geo':
D_diag = np.array([d1 * d2 for d1 in D1 for d2 in D2])
kmiddle = np.diag(weight * D_diag)
kmiddle = np.identity(len(kmiddle)) - weight * kmiddle
kmiddle = np.linalg.inv(kmiddle)
return np.dot(np.dot(kl, kmiddle), kl.T)[0, 0]


###############################################################################
def _randomwalkkernel_kron(G1, G2, node_label, edge_label):
"""Calculate walk graph kernels up to n between 2 graphs using nearest Kronecker product approximation method.

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.

Return
------
kernel : float
Kernel between 2 graphs.
"""
pass


###############################################################################
def getLabels(Gn, node_label, edge_label, directed):
"""Get symbolic labels of a graph dataset, where vertex labels are dealt
with by concatenating them to the edge labels of adjacent edges.
"""
label_list = []
label_set = set()
for g in Gn:
label_g = {}
for e in g.edges(data=True):
nl1 = g.node[e[0]][node_label]
nl2 = g.node[e[1]][node_label]
if not directed and nl1 > nl2:
nl1, nl2 = nl2, nl1
label = (nl1, e[2][edge_label], nl2)
label_g[(e[0], e[1])] = label
label_list.append(label_g)
label_set = set([l for lg in label_list for l in lg.values()])
return label_list, len(label_set)


def filterGramMatrix(gmt, label_dict, label, directed):
"""Compute (the transpose of) the Gram matrix filtered by a label.
"""
gmf = np.zeros(gmt.shape)
for (n1, n2), l in label_dict.items():
if l == label:
gmf[n2, n1] = gmt[n2, n1]
if not directed:
gmf[n1, n2] = gmt[n1, n2]
return gmf


def computeVK(g1, g2, ds_attrs, node_kernels, node_label):
'''Compute vertex kernels between vertices of two graphs.
'''
vk_dict = {} # shortest path matrices dict
if ds_attrs['node_labeled']:
# node symb and non-synb labeled
if ds_attrs['node_attr_dim'] > 0:
kn = node_kernels['mix']
for n1 in g1.nodes(data=True):
for n2 in g2.nodes(data=True):
vk_dict[(n1[0], n2[0])] = kn(
n1[1][node_label], n2[1][node_label],
n1[1]['attributes'], n2[1]['attributes'])
# node symb labeled
else:
kn = node_kernels['symb']
for n1 in g1.nodes(data=True):
for n2 in g2.nodes(data=True):
vk_dict[(n1[0], n2[0])] = kn(n1[1][node_label],
n2[1][node_label])
else:
# node non-synb labeled
if ds_attrs['node_attr_dim'] > 0:
kn = node_kernels['nsymb']
for n1 in g1.nodes(data=True):
for n2 in g2.nodes(data=True):
vk_dict[(n1[0], n2[0])] = kn(n1[1]['attributes'],
n2[1]['attributes'])
# node unlabeled
else:
pass
return vk_dict


def computeW(g1, g2, vk_dict, ds_attrs, edge_kernels, edge_label):
'''Compute weight matrix of the direct product graph.
'''
w_dim = nx.number_of_nodes(g1) * nx.number_of_nodes(g2)
w_times = np.zeros((w_dim, w_dim))
if vk_dict: # node labeled
if ds_attrs['is_directed']:
if ds_attrs['edge_labeled']:
# edge symb and non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['mix']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label],
e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])]
# edge symb labeled
else:
ke = edge_kernels['symb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])]
else:
# edge non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['nsymb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])]
# edge unlabeled
else:
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* vk_dict[(e1[1], e2[1])]
else: # undirected
if ds_attrs['edge_labeled']:
# edge symb and non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['mix']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label],
e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])] \
+ vk_dict[(e1[0], e2[1])] \
* ek_temp * vk_dict[(e1[1], e2[0])]
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
# edge symb labeled
else:
ke = edge_kernels['symb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])] \
+ vk_dict[(e1[0], e2[1])] \
* ek_temp * vk_dict[(e1[1], e2[0])]
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
else:
# edge non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['nsymb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* ek_temp * vk_dict[(e1[1], e2[1])] \
+ vk_dict[(e1[0], e2[1])] \
* ek_temp * vk_dict[(e1[1], e2[0])]
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
# edge unlabeled
else:
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = vk_dict[(e1[0], e2[0])] \
* vk_dict[(e1[1], e2[1])] \
+ vk_dict[(e1[0], e2[1])] \
* vk_dict[(e1[1], e2[0])]
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
else: # node unlabeled
if ds_attrs['is_directed']:
if ds_attrs['edge_labeled']:
# edge symb and non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['mix']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label],
e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
# edge symb labeled
else:
ke = edge_kernels['symb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
else:
# edge non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['nsymb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
# edge unlabeled
else:
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = 1
else: # undirected
if ds_attrs['edge_labeled']:
# edge symb and non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['mix']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label],
e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
# edge symb labeled
else:
ke = edge_kernels['symb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2][edge_label], e2[2][edge_label])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
else:
# edge non-synb labeled
if ds_attrs['edge_attr_dim'] > 0:
ke = edge_kernels['nsymb']
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
ek_temp = ke(e1[2]['attributes'], e2[2]['attributes'])
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = ek_temp
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
# edge unlabeled
else:
for e1 in g1.edges(data=True):
for e2 in g2.edges(data=True):
w_idx = (e1[0] * nx.number_of_nodes(g2) + e2[0],
e1[1] * nx.number_of_nodes(g2) + e2[1])
w_times[w_idx] = 1
w_times[w_idx[1], w_idx[0]] = w_times[w_idx[0], w_idx[1]]
w_idx2 = (e1[0] * nx.number_of_nodes(g2) + e2[1],
e1[1] * nx.number_of_nodes(g2) + e2[0])
w_times[w_idx2[0], w_idx2[1]] = w_times[w_idx[0], w_idx[1]]
w_times[w_idx2[1], w_idx2[0]] = w_times[w_idx[0], w_idx[1]]
return w_times, w_dim

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