-
Notifications
You must be signed in to change notification settings - Fork 3
/
markov.py
277 lines (266 loc) · 11.2 KB
/
markov.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
import os.path as osp
import argparse
import sys,time
import numpy as np
from tqdm import tqdm
import torch, random
from torch_sparse import spspmm
from torch_geometric.utils import add_remaining_self_loops, to_dense_adj, dense_to_sparse
from torch_scatter import scatter_add
from utils import computeHomophily, newEdges, mixingCommunityScore
debug_on = False
def markov_normalization(edge_index, edge_weight, num_nodes, ntype = 'col'):
if ntype == 'col':
_, col = edge_index
deg = scatter_add(edge_weight, col, dim=0, dim_size=num_nodes)
deg_inv = 1. / deg
deg_inv[deg_inv == float('inf')] = 0
edge_weight = edge_weight * deg_inv[col]
elif ntype == 'row':
row, _ = edge_index
deg = scatter_add(edge_weight, row, dim=0, dim_size=num_nodes)
deg_inv = 1. / deg
deg_inv[deg_inv == float('inf')] = 0
edge_weight = edge_weight * deg_inv[row]
return edge_index, edge_weight
def markov_process_agg_sparse(data, eps, inflate, nlayers, row_normalization = True, debug = True):
# sparse operations
start = time.time()
ei, ew = data.edge_index, data.edge_attr
if ew is None or len(ew) == 0:
ew = torch.ones(ei.shape[1])
medge_index = []
medge_weight = []
medge_index.append(ei)
medge_weight.append(ew)
for i in range(nlayers-1):
ei, ew = spspmm(ei, ew, ei, ew, len(data.x), len(data.x), len(data.x))
ew = torch.pow(ew, inflate)
# normalization of matrix
if row_normalization:
ei, ew = markov_normalization(ei, ew, len(data.x), 'row')
else:
ei, ew = markov_normalization(ei, ew, len(data.x), 'col')
# pruning stage
remaining_edge_idx = torch.nonzero(ew >= eps).flatten()
ei = ei[:,remaining_edge_idx]
ew = ew[remaining_edge_idx]
if ei.shape[1] < 1:
print("No more edges..! stopping after ", i, "layers")
break
# normalization
if row_normalization:
ei, ew = markov_normalization(ei, ew, len(data.x), 'row')
else:
ei, ew = markov_normalization(ei, ew, len(data.x), 'col')
# store layer-wise edges
medge_index.append(ei)
medge_weight.append(ew)
if debug_on:
print("layer ", i+1, "(after sparsification) edge_index size:", ei.shape, "homophily:", computeHomophily(data, ei))
print("Community Mixing Param:", mixingCommunityScore(data, ei), "New Edges:", newEdges(data, ei))
if nlayers > len(medge_index):
print("Use less number of layers for the given", eps, " threshold, maximum:", len(medge_index), "layers")
sys.exit(1)
end = time.time()
if debug:
print("Time required for sparse markov process:", end - start, "seconds")
return (medge_index, medge_weight)
def markov_process_agg(data, eps, inflate, nlayers, row_normalization = True, keepmax = True, debug = True):
start = time.time()
A = to_dense_adj(edge_index = data.edge_index, batch = None, edge_attr = data.edge_attr, max_num_nodes = int(data.x.shape[0]))[0]
(ei, ew) = dense_to_sparse(A)
medge_index = []
medge_weight = []
medge_index.append(ei)
medge_weight.append(ew)
if debug:
print("layer 0", "edge_index initial size:", data.edge_index.shape)
AP = A.clone()
for i in range(nlayers-1):
A = torch.mm(A, A)
A = torch.pow(A, inflate)
(ei, ew) = dense_to_sparse(A)
if debug_on:
print("layer ", i+1, " (after mul and pow) edge_index size:", ei.shape)
# normalization
if row_normalization:
ei, ew = markov_normalization(ei, ew, A.shape[0], 'row')
else:
ei, ew = markov_normalization(ei, ew, A.shape[0], 'col')
if keepmax:
# sparsification threshold
remaining_edge_idx = torch.nonzero(ew >= eps).flatten()
ei = ei[:,remaining_edge_idx]
ew = ew[remaining_edge_idx]
else:
# keep max value in each row of the adj matrix
A = to_dense_adj(edge_index = ei, batch = None, edge_attr = ew, max_num_nodes = int(data.x.shape[0]))[0]
for i in range(len(A)):
idx = torch.nonzero(A[i] < eps).flatten()
if len(idx) == len(A[i]):
idmax = torch.argmax(A[i])
valmax = torch.max(A[i])
A[i, idx] = 0
A[i, idmax] = valmax
else:
A[i, idx] = 0
(ei, ew) = dense_to_sparse(A)
if ei.shape[1] < 1:
print("No more edges..! stopping after ", i, "layers")
break
#normalization
if row_normalization:
edge_index2, edge_weight2 = markov_normalization(ei, ew, A.shape[0], 'row')
else:
edge_index2, edge_weight2 = markov_normalization(ei, ew, A.shape[0], 'col')
A = to_dense_adj(edge_index = edge_index2, batch = None, edge_attr = edge_weight2, max_num_nodes = int(data.x.shape[0]))[0]
if debug_on:
print("layer ", i+1, "(after sparsification) edge_index size:", edge_index2.shape)
medge_index.append(edge_index2)
medge_weight.append(edge_weight2)
if nlayers > len(medge_index):
print("Use less number of layers for the given", eps, " threshold, maximum:", len(medge_index), "layers")
sys.exit(1)
end = time.time()
if debug:
print("Time required for dense markov process:", end - start, "seconds")
return (medge_index, medge_weight)
def markov_process_disj_sparse(data, eps, inflate, nlayers, row_normalization = True, keepmax = True, debug = True):
start = time.time()
ei, ew = data.edge_index, data.edge_attr
if ew is None or len(ew) == 0:
ew = torch.ones(ei.shape[1])
medge_index = []
medge_weight = []
medge_index.append(ei)
medge_weight.append(ew)
prev_edge_index = ei
# markov process converges less than 30 iterations for the tested graphs
for i in range(30):
# sparse matrix-matrix multiplication
ei, ew = spspmm(ei, ew, ei, ew, len(data.x), len(data.x), len(data.x))
ew = torch.pow(ew, inflate)
# normalization of matrix
if row_normalization:
ei, ew = markov_normalization(ei, ew, len(data.x), 'row')
else:
ei, ew = markov_normalization(ei, ew, len(data.x), 'col')
# pruning stage
remaining_edge_idx = torch.nonzero(ew >= eps).flatten()
ei = ei[:,remaining_edge_idx]
ew = ew[remaining_edge_idx]
if ei.shape[1] < 1:
print("No more edges..! stopping after ", i, "layers")
break
# normalization
if row_normalization:
ei, ew = markov_normalization(ei, ew, len(data.x), 'row')
else:
ei, ew = markov_normalization(ei, ew, len(data.x), 'col')
# store layer-wise edges
medge_index.append(ei)
medge_weight.append(ew)
if debug_on:
print("layer ", i+1, "(after sparsification) edge_index size:", ei.shape)
if ei[0].shape == prev_edge_index[0].shape:
print("early stopping markov process due to converged number of edges.")
break
prev_edge_index = ei
if nlayers > len(medge_index):
print("Use less number of layers for the given", eps, " threshold, maximum:", len(medge_index), "layers")
sys.exit(1)
# taking l matrices from k markov matrices
mei = []
mew = []
step = len(medge_index) // nlayers
idx = step
mei.append(medge_index[0])
mew.append(medge_weight[0])
for l in range(1, nlayers-1):
mei.append(medge_index[idx])
mew.append(medge_weight[idx])
idx += step
mei.append(medge_index[len(medge_index)-1])
mew.append(medge_weight[len(medge_index)-1])
end = time.time()
if debug:
print("Time required for sparse markov process:", end - start, "seconds")
return (mei, mew)
def markov_process_disj(data, eps, inflate, nlayers, row_normalization = True, keepmax = True, debug = True):
start = time.time()
A = to_dense_adj(edge_index = data.edge_index, batch = None, edge_attr = data.edge_attr, max_num_nodes = int(data.x.shape[0]))[0]
(ei, ew) = dense_to_sparse(A)
medge_index = []
medge_weight = []
medge_index.append(ei)
medge_weight.append(ew)
if debug:
print("layer 0", "edge_index initial size:", data.edge_index.shape)
AP = A.clone()
prev_edge_index = ei
for i in range(30):
A = torch.mm(A, A)
A = torch.pow(A, inflate)
(ei, ew) = dense_to_sparse(A)
if debug_on:
print("layer ", i+1, " (after mul and pow) edge_index size:", ei.shape)
# normalization
if row_normalization:
ei, ew = markov_normalization(ei, ew, A.shape[0], 'row')
else:
ei, ew = markov_normalization(ei, ew, A.shape[0], 'col')
if keepmax:
# sparsification threshold
remaining_edge_idx = torch.nonzero(ew >= eps).flatten()
ei = ei[:,remaining_edge_idx]
ew = ew[remaining_edge_idx]
else:
# keep max value in each row of the adj matrix
A = to_dense_adj(edge_index = ei, batch = None, edge_attr = ew, max_num_nodes = int(data.x.shape[0]))[0]
for i in range(len(A)):
idx = torch.nonzero(A[i] < eps).flatten()
if len(idx) == len(A[i]):
idmax = torch.argmax(A[i])
valmax = torch.max(A[i])
A[i, idx] = 0
A[i, idmax] = valmax
else:
A[i, idx] = 0
(ei, ew) = dense_to_sparse(A)
if ei.shape[1] < 1:
print("No more edges..! stopping after ", i, "layers")
break
#normalization
if row_normalization:
edge_index2, edge_weight2 = markov_normalization(ei, ew, A.shape[0], 'row')
else:
edge_index2, edge_weight2 = markov_normalization(ei, ew, A.shape[0], 'col')
A = to_dense_adj(edge_index = edge_index2, batch = None, edge_attr = edge_weight2, max_num_nodes = int(data.x.shape[0]))[0]
if debug_on:
print("layer ", i+1, "(after sparsification) edge_index size:", edge_index2.shape)
medge_index.append(edge_index2)
medge_weight.append(edge_weight2)
if edge_index2[0].shape == prev_edge_index[0].shape:
print("early stopping markov process due to converged number of edges.")
break
prev_edge_index = edge_index2
if nlayers > len(medge_index):
print("Use less number of layers for the given", eps, " threshold, maximum:", len(medge_index), "layers")
sys.exit(1)
mei = []
mew = []
step = len(medge_index) // nlayers
idx = step
mei.append(medge_index[0])
mew.append(medge_weight[0])
for l in range(1, nlayers-1):
mei.append(medge_index[idx])
mew.append(medge_weight[idx])
idx += step
mei.append(medge_index[len(medge_index)-1])
mew.append(medge_weight[len(medge_index)-1])
end = time.time()
if debug:
print("Time required for dense markov process:", end - start, "seconds")
return (mei, mew)