New translations spectral_decomposition.py (Chinese Simplified)

lang/zh/gklearn/kernels/spectral_decomposition.py

@@ -0,0 +1,283 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Aug 20 16:12:45 2020
+
+@author: ljia
+
+@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 sys
+from tqdm import tqdm
+import numpy as np
+import networkx as nx
+from scipy.sparse import kron
+from gklearn.utils.parallel import parallel_gm, parallel_me
+from gklearn.kernels import RandomWalk
+
+
+class SpectralDecomposition(RandomWalk):
+	
+	
+	def __init__(self, **kwargs):
+		RandomWalk.__init__(self, **kwargs)
+		self._sub_kernel = kwargs.get('sub_kernel', None)
+		
+
+	def _compute_gm_series(self):
+		self._check_edge_weight(self._graphs)
+		self._check_graphs(self._graphs)
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored. Only works for undirected graphs.')
+				
+		# compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))		
+		
+		if self._q == None:
+			# precompute the spectral decomposition of each graph.
+			P_list = []
+			D_list = []
+			if self._verbose >= 2:
+				iterator = tqdm(self._graphs, desc='spectral decompose', file=sys.stdout)
+			else:
+				iterator = self._graphs
+			for G in iterator:
+				# 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, self._edge_weight).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 self._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 self._graphs]
+#			q_T_list = [q.T for q in q_list]
+
+				from itertools import combinations_with_replacement
+				itr = combinations_with_replacement(range(0, len(self._graphs)), 2)
+				if self._verbose >= 2:
+					iterator = tqdm(itr, desc='calculating kernels', file=sys.stdout)
+				else:
+					iterator = itr
+					
+				for i, j in iterator:
+					kernel = self.__kernel_do(q_T_list[i], q_T_list[j], P_list[i], P_list[j], D_list[i], D_list[j], self._weight, self._sub_kernel)
+					gram_matrix[i][j] = kernel
+					gram_matrix[j][i] = kernel
+			
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return gram_matrix
+			
+			
+	def _compute_gm_imap_unordered(self):
+		self._check_edge_weight(self._graphs)
+		self._check_graphs(self._graphs)
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored. Only works for undirected graphs.')
+				
+		# compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))		
+		
+		if self._q == None:
+			# precompute the spectral decomposition of each graph.
+			P_list = []
+			D_list = []
+			if self._verbose >= 2:
+				iterator = tqdm(self._graphs, desc='spectral decompose', file=sys.stdout)
+			else:
+				iterator = self._graphs
+			for G in iterator:
+				# 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, self._edge_weight).todense().transpose()
+				ew, ev = np.linalg.eig(A)
+				D_list.append(ew)
+				P_list.append(ev) # @todo: parallel?
+
+			if self._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 self._graphs] # @todo: parallel?
+				
+				def init_worker(q_T_list_toshare, P_list_toshare, D_list_toshare):
+					global G_q_T_list, G_P_list, G_D_list
+					G_q_T_list = q_T_list_toshare
+					G_P_list = P_list_toshare
+					G_D_list = D_list_toshare
+					
+				do_fun = self._wrapper_kernel_do					
+				parallel_gm(do_fun, gram_matrix, self._graphs, init_worker=init_worker, 
+							glbv=(q_T_list, P_list, D_list), n_jobs=self._n_jobs, verbose=self._verbose)
+
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return gram_matrix
+	
+	
+	def _compute_kernel_list_series(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1])
+		self._check_graphs(g_list + [g1])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored. Only works for undirected graphs.')
+							
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+		
+		if self._q == None:
+			# precompute the spectral decomposition of each graph.
+			A1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			D1, P1 = np.linalg.eig(A1)
+			P_list = []
+			D_list = []
+			if self._verbose >= 2:
+				iterator = tqdm(range(len(g_list)), desc='spectral decompose', file=sys.stdout)
+			else:
+				iterator = range(len(g_list))
+			for G in iterator:
+				# 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, self._edge_weight).todense().transpose()
+				ew, ev = np.linalg.eig(A)
+				D_list.append(ew)
+				P_list.append(ev)
+
+			if self._p == None: # p is uniform distribution as default.
+				q_T1 = 1 / nx.number_of_nodes(g1)
+				q_T_list = [np.full((1, nx.number_of_nodes(G)), 1 / nx.number_of_nodes(G)) for G in g_list]
+				if self._verbose >= 2:
+					iterator = tqdm(range(len(g_list)), desc='calculating kernels', file=sys.stdout)
+				else:
+					iterator = range(len(g_list))
+					
+				for i in iterator:
+					kernel = self.__kernel_do(q_T1, q_T_list[i], P1, P_list[i], D1, D_list[i], self._weight, self._sub_kernel)
+					kernel_list[i] = kernel
+					
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel_list
+	
+	
+	def _compute_kernel_list_imap_unordered(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1])
+		self._check_graphs(g_list + [g1])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored. Only works for undirected graphs.')
+				
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+		
+		if self._q == None:
+			# precompute the spectral decomposition of each graph.
+			A1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			D1, P1 = np.linalg.eig(A1)
+			P_list = []
+			D_list = []
+			if self._verbose >= 2:
+				iterator = tqdm(range(len(g_list)), desc='spectral decompose', file=sys.stdout)
+			else:
+				iterator = range(len(g_list))
+			for G in iterator:
+				# 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, self._edge_weight).todense().transpose()
+				ew, ev = np.linalg.eig(A)
+				D_list.append(ew)
+				P_list.append(ev) # @todo: parallel?
+
+			if self._p == None: # p is uniform distribution as default.
+				q_T1 = 1 / nx.number_of_nodes(g1)
+				q_T_list = [np.full((1, nx.number_of_nodes(G)), 1 / nx.number_of_nodes(G)) for G in g_list] # @todo: parallel?
+				
+				def init_worker(q_T1_toshare, P1_toshare, D1_toshare, q_T_list_toshare, P_list_toshare, D_list_toshare):
+					global G_q_T1, G_P1, G_D1, G_q_T_list, G_P_list, G_D_list
+					G_q_T1 = q_T1_toshare
+					G_P1 = P1_toshare
+					G_D1 = D1_toshare
+					G_q_T_list = q_T_list_toshare
+					G_P_list = P_list_toshare
+					G_D_list = D_list_toshare
+
+				do_fun = self._wrapper_kernel_list_do	
+				
+				def func_assign(result, var_to_assign):	
+					var_to_assign[result[0]] = result[1]
+				itr = range(len(g_list))
+				len_itr = len(g_list)
+				parallel_me(do_fun, func_assign, kernel_list, itr, len_itr=len_itr,
+					init_worker=init_worker, glbv=(q_T1, P1, D1, q_T_list, P_list, D_list), method='imap_unordered', n_jobs=self._n_jobs, itr_desc='calculating kernels', verbose=self._verbose)
+			
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel_list
+
+
+	def _wrapper_kernel_list_do(self, itr):
+		return itr, self._kernel_do(G_q_T1, G_q_T_list[itr], G_P1, G_P_list[itr], G_D1, G_D_list[itr], self._weight, self._sub_kernel)
+	
+	
+	def _compute_single_kernel_series(self, g1, g2):
+		self._check_edge_weight([g1] + [g2])
+		self._check_graphs([g1] + [g2])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored. Only works for undirected graphs.')
+		
+		if self._q == None:
+			# precompute the spectral decomposition of each graph.
+			A1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			D1, P1 = np.linalg.eig(A1)
+			A2 = nx.adjacency_matrix(g2, self._edge_weight).todense().transpose()
+			D2, P2 = np.linalg.eig(A2)
+
+			if self._p == None: # p is uniform distribution as default.
+				q_T1 = 1 / nx.number_of_nodes(g1)
+				q_T2 = 1 / nx.number_of_nodes(g2)
+				kernel = self.__kernel_do(q_T1, q_T2, P1, P2, D1, D2, self._weight, self._sub_kernel)
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel		
+	
+	
+	def __kernel_do(self, 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 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 _wrapper_kernel_do(self, itr):
+		i = itr[0]
+		j = itr[1]
+		return i, j, self.__kernel_do(G_q_T_list[i], G_q_T_list[j], G_P_list[i], G_P_list[j], G_D_list[i], G_D_list[j], self._weight, self._sub_kernel)