New translations conjugate_gradient.py (Chinese Simplified)

lang/zh/gklearn/kernels/conjugate_gradient.py

@@ -0,0 +1,322 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Aug 20 16:09:51 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 identity
+from scipy.sparse.linalg import cg
+from gklearn.utils.parallel import parallel_gm, parallel_me
+from gklearn.kernels import RandomWalkMeta
+from gklearn.utils.utils import compute_vertex_kernels
+
+
+class ConjugateGradient(RandomWalkMeta):
+	
+	
+	def __init__(self, **kwargs):
+		super().__init__(**kwargs)
+		self._node_kernels = kwargs.get('node_kernels', None)
+		self._edge_kernels = kwargs.get('edge_kernels', None)
+		self._node_labels = kwargs.get('node_labels', [])
+		self._edge_labels = kwargs.get('edge_labels', [])
+		self._node_attrs = kwargs.get('node_attrs', [])
+		self._edge_attrs = kwargs.get('edge_attrs', [])
+		
+
+	def _compute_gm_series(self):
+		self._check_edge_weight(self._graphs, self._verbose)
+		self._check_graphs(self._graphs)
+			
+		lmda = self._weight
+				
+		# Compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))		
+		
+		# Reindex nodes using consecutive integers for the convenience of kernel computation.
+		if self._verbose >= 2:
+			iterator = tqdm(self._graphs, desc='Reindex vertices', file=sys.stdout)
+		else:
+			iterator = self._graphs
+		self._graphs = [nx.convert_node_labels_to_integers(g, first_label=0, label_attribute='label_orignal') for g in iterator]
+		
+		if self._p is None and self._q is None: # p and q are uniform distributions as default.
+		
+			from itertools import combinations_with_replacement
+			itr = combinations_with_replacement(range(0, len(self._graphs)), 2)
+			if self._verbose >= 2:
+				iterator = tqdm(itr, desc='Computing kernels', file=sys.stdout)
+			else:
+				iterator = itr
+				
+			for i, j in iterator:
+				kernel = self._kernel_do(self._graphs[i], self._graphs[j], lmda)
+				gram_matrix[i][j] = kernel
+				gram_matrix[j][i] = kernel
+
+		else: # @todo
+			pass
+				
+		return gram_matrix
+			
+			
+	def _compute_gm_imap_unordered(self):
+		self._check_edge_weight(self._graphs, self._verbose)
+		self._check_graphs(self._graphs)
+				
+		# Compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))
+		
+		# @todo: parallel this.
+		# Reindex nodes using consecutive integers for the convenience of kernel computation.
+		if self._verbose >= 2:
+			iterator = tqdm(self._graphs, desc='Reindex vertices', file=sys.stdout)
+		else:
+			iterator = self._graphs
+		self._graphs = [nx.convert_node_labels_to_integers(g, first_label=0, label_attribute='label_orignal') for g in iterator]
+		
+		if self._p is None and self._q is None: # p and q are uniform distributions as default.
+
+			def init_worker(gn_toshare):
+				global G_gn
+				G_gn = gn_toshare
+				
+			do_fun = self._wrapper_kernel_do
+				
+			parallel_gm(do_fun, gram_matrix, self._graphs, init_worker=init_worker, 
+						glbv=(self._graphs,), n_jobs=self._n_jobs, verbose=self._verbose)
+
+		else: # @todo
+			pass
+				
+		return gram_matrix
+	
+	
+	def _compute_kernel_list_series(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1], self._verbose)
+		self._check_graphs(g_list + [g1])
+			
+		lmda = self._weight
+				
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+
+		# Reindex nodes using consecutive integers for the convenience of kernel computation.
+		g1 = nx.convert_node_labels_to_integers(g1, first_label=0, label_attribute='label_orignal')
+		if self._verbose >= 2:
+			iterator = tqdm(g_list, desc='Reindex vertices', file=sys.stdout)
+		else:
+			iterator = g_list
+		g_list = [nx.convert_node_labels_to_integers(g, first_label=0, label_attribute='label_orignal') for g in iterator]
+		
+		if self._p is None and self._q is None: # p and q are uniform distributions as default.
+
+			if self._verbose >= 2:
+				iterator = tqdm(range(len(g_list)), desc='Computing kernels', file=sys.stdout)
+			else:
+				iterator = range(len(g_list))
+				
+			for i in iterator:
+				kernel = self._kernel_do(g1, g_list[i], lmda)
+				kernel_list[i] = kernel
+
+		else: # @todo
+			pass
+				
+		return kernel_list
+	
+	
+	def _compute_kernel_list_imap_unordered(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1], self._verbose)
+		self._check_graphs(g_list + [g1])
+				
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+		
+		# Reindex nodes using consecutive integers for the convenience of kernel computation.
+		g1 = nx.convert_node_labels_to_integers(g1, first_label=0, label_attribute='label_orignal')
+		# @todo: parallel this.
+		if self._verbose >= 2:
+			iterator = tqdm(g_list, desc='Reindex vertices', file=sys.stdout)
+		else:
+			iterator = g_list
+		g_list = [nx.convert_node_labels_to_integers(g, first_label=0, label_attribute='label_orignal') for g in iterator]
+		
+		if self._p is None and self._q is None: # p and q are uniform distributions as default.
+
+			def init_worker(g1_toshare, g_list_toshare):
+				global G_g1, G_g_list
+				G_g1 = g1_toshare
+				G_g_list = g_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=(g1, g_list), method='imap_unordered', 
+				n_jobs=self._n_jobs, itr_desc='Computing kernels', verbose=self._verbose)
+			
+		else: # @todo
+			pass
+				
+		return kernel_list
+
+
+	def _wrapper_kernel_list_do(self, itr):
+		return itr, self._kernel_do(G_g1, G_g_list[itr], self._weight)
+	
+	
+	def _compute_single_kernel_series(self, g1, g2):
+		self._check_edge_weight([g1] + [g2], self._verbose)
+		self._check_graphs([g1] + [g2])
+			
+		lmda = self._weight
+		
+		# Reindex nodes using consecutive integers for the convenience of kernel computation.
+		g1 = nx.convert_node_labels_to_integers(g1, first_label=0, label_attribute='label_orignal')
+		g2 = nx.convert_node_labels_to_integers(g2, first_label=0, label_attribute='label_orignal')
+		
+		if self._p is None and self._q is None: # p and q are uniform distributions as default.
+			kernel = self._kernel_do(g1, g2, lmda)
+
+		else: # @todo
+			pass
+				
+		return kernel		
+	
+	
+	def _kernel_do(self, g1, g2, lmda):
+		
+		# Frist, compute kernels between all pairs of nodes using the 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 = self._compute_vertex_kernels(g1, g2)
+							   
+		# Compute the weight matrix of the direct product graph.   
+		w_times, w_dim = self._compute_weight_matrix(g1, g2, vk_dict)															
+		# 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 _wrapper_kernel_do(self, itr):
+		i = itr[0]
+		j = itr[1]
+		return i, j, self._kernel_do(G_gn[i], G_gn[j], self._weight)
+	
+	
+	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 _compute_vertex_kernels(self, g1, g2):
+		"""Compute vertex kernels between vertices of two graphs.
+		"""
+		return compute_vertex_kernels(g1, g2, self._node_kernels, node_labels=self._node_labels, node_attrs=self._node_attrs)
+	
+	
+	# @todo: move if out to make it faster.
+	# @todo: node/edge kernels use direct function rather than dicts.
+	def _compute_weight_matrix(self, g1, g2, vk_dict):
+		"""Compute the weight matrix of the direct product graph.
+		"""
+		# Define edge kernels.
+		def compute_ek_11(e1, e2, ke):
+			e1_labels = [e1[2][el] for el in self._edge_labels]
+			e2_labels = [e2[2][el] for el in self._edge_labels]
+			e1_attrs = [e1[2][ea] for ea in self._edge_attrs]
+			e2_attrs = [e2[2][ea] for ea in self._edge_attrs]
+			return ke(e1_labels, e2_labels, e1_attrs, e2_attrs)
+		
+		def compute_ek_10(e1, e2, ke):
+			e1_labels = [e1[2][el] for el in self._edge_labels]
+			e2_labels = [e2[2][el] for el in self._edge_labels]
+			return ke(e1_labels, e2_labels)
+		
+		def compute_ek_01(e1, e2, ke):
+			e1_attrs = [e1[2][ea] for ea in self._edge_attrs]
+			e2_attrs = [e2[2][ea] for ea in self._edge_attrs]
+			return ke(e1_attrs, e2_attrs)
+		
+		def compute_ek_00(e1, e2, ke):
+			return 1
+			
+		# Select the proper edge kernel.
+		if len(self._edge_labels) > 0:
+			# edge symb and non-synb labeled
+			if len(self._edge_attrs) > 0:
+				ke = self._edge_kernels['mix']
+				ek_temp = compute_ek_11
+			# edge symb labeled
+			else:
+				ke = self._edge_kernels['symb']
+				ek_temp = compute_ek_10
+		else:
+			# edge non-synb labeled
+			if len(self._edge_attrs) > 0:
+				ke = self._edge_kernels['nsymb']
+				ek_temp = compute_ek_01
+			# edge unlabeled
+			else:
+				ke = None
+				ek_temp = compute_ek_00 # @todo: check how much slower is this.
+			
+		# Compute the weight matrix.
+		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 self._ds_infos['directed']:
+				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])] * ek_temp(e1, e2, ke) * vk_dict[(e1[1], e2[1])]
+			else: # undirected
+				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])] * ek_temp(e1, e2, ke) * vk_dict[(e1[1], e2[1])] + vk_dict[(e1[0], e2[1])] * ek_temp(e1, e2, ke) * 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 self._ds_infos['directed']:
+				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] = ek_temp(e1, e2, ke)
+			else: # undirected
+				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] = ek_temp(e1, e2, ke)
+						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