forked from nzhiltsov/Ext-RESCAL
/
extrescal.py
248 lines (212 loc) · 8.6 KB
/
extrescal.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
import logging, time, argparse
from numpy import dot, kron, array, eye, savetxt
from numpy.linalg import qr, pinv, norm, inv
from numpy.random import rand
from scipy.sparse.linalg import eigsh
import numpy as np
from commonFunctions import squareFrobeniusNormOfSparse, squareFrobeniusNormOfSparseBoolean, fitNormWithoutNormX, loadX
from extrescalFunctions import updateA, updateV, matrixFitNormWithoutNormD, loadD
__DEF_MAXITER = 50
__DEF_PREHEATNUM = 1
__DEF_INIT = 'nvecs'
__DEF_PROJ = True
__DEF_CONV = 1e-5
__DEF_LMBDA = 0
def rescal(X, D, rank, **kwargs):
"""
RESCAL
Factors a three-way tensor X such that each frontal slice
X_k = A * R_k * A.T. The frontal slices of a tensor are
N x N matrices that correspond to the adjacency matrices
of the relational graph for a particular relation.
For a full description of the algorithm see:
Maximilian Nickel, Volker Tresp, Hans-Peter-Kriegel,
"A Three-Way Model for Collective Learning on Multi-Relational Data",
ICML 2011, Bellevue, WA, USA
Parameters
----------
X : list
List of frontal slices X_k of the tensor X. The shape of each X_k is ('N', 'N')
D : matrix
A sparse matrix involved in the tensor factorization (aims to incorporate
the entity-term matrix aka document-term matrix)
rank : int
Rank of the factorization
lmbda : float, optional
Regularization parameter for A and R_k factor matrices. 0 by default
init : string, optional
Initialization method of the factor matrices. 'nvecs' (default)
initializes A based on the eigenvectors of X. 'random' initializes
the factor matrices randomly.
proj : boolean, optional
Whether or not to use the QR decomposition when computing R_k.
True by default
maxIter : int, optional
Maximium number of iterations of the ALS algorithm. 50 by default.
conv : float, optional
Stop when residual of factorization is less than conv. 1e-5 by default
Returns
-------
A : ndarray
matrix of latent embeddings for entities A
R : list
list of 'M' arrays of shape ('rank', 'rank') corresponding to the factor matrices R_k
f : float
function value of the factorization
iter : int
number of iterations until convergence
exectimes : ndarray
execution times to compute the updates in each iteration
V : ndarray
matrix of latent embeddings for words V
"""
# init options
ainit = kwargs.pop('init', __DEF_INIT)
proj = kwargs.pop('proj', __DEF_PROJ)
maxIter = kwargs.pop('maxIter', __DEF_MAXITER)
conv = kwargs.pop('conv', __DEF_CONV)
lmbda = kwargs.pop('lmbda', __DEF_LMBDA)
preheatnum = kwargs.pop('preheatnum', __DEF_PREHEATNUM)
if not len(kwargs) == 0:
raise ValueError( 'Unknown keywords (%s)' % (kwargs.keys()) )
sz = X[0].shape
dtype = X[0].dtype
n = sz[0]
_log.debug('[Config] rank: %d | maxIter: %d | conv: %7.1e | lmbda: %7.1e' % (rank,
maxIter, conv, lmbda))
# precompute norms of X
normX = [squareFrobeniusNormOfSparseBoolean(M) for M in X]
sumNormX = sum(normX)
normD = squareFrobeniusNormOfSparse(D)
_log.debug('[Algorithm] The tensor norm: %.5f' % sumNormX)
_log.debug('[Algorithm] The extended matrix norm: %.5f' % normD)
# initialize A
if ainit == 'random':
_log.debug('[Algorithm] The random initialization will be performed.')
A = array(rand(n, rank), dtype=np.float64)
elif ainit == 'nvecs':
_log.debug('[Algorithm] The eigenvector based initialization will be performed.')
tic = time.clock()
avgX = X[0] + X[0].T
for i in range(1, len(X)):
avgX = avgX + (X[i] + X[i].T)
toc = time.clock()
elapsed = toc - tic
_log.debug('Initializing tensor slices by summation required secs: %.5f' % elapsed)
tic = time.clock()
eigvals, A = eigsh(avgX.tocsc(), rank)
toc = time.clock()
elapsed = toc - tic
_log.debug('eigenvector decomposition required secs: %.5f' % elapsed)
else :
raise 'Unknown init option ("%s")' % ainit
# initialize R
if proj:
Q, A2 = qr(A)
X2 = __projectSlices(X, Q)
R = __updateR(X2, A2, lmbda)
else :
raise 'Projection via QR decomposition is required; pass proj=true'
_log.debug('[Algorithm] Finished initialization.')
# compute factorization
fit = fitchange = fitold = 0
exectimes = []
for iterNum in xrange(maxIter):
tic = time.clock()
V = updateV(A, D, lmbda)
A = updateA(X, A, R, V, D, lmbda)
if proj:
Q, A2 = qr(A)
X2 = __projectSlices(X, Q)
R = __updateR(X2, A2, lmbda)
else :
raise 'Projection via QR decomposition is required; pass proj=true'
# compute fit values
fit = 0
tensorFit = 0
regularizedFit = 0
extRegularizedFit = 0
regRFit = 0
fitDAV = 0
if iterNum >= preheatnum:
if lmbda != 0:
for i in xrange(len(R)):
regRFit += norm(R[i])**2
regularizedFit = lmbda*(norm(A)**2) + lmbda*regRFit
if lmbda != 0:
extRegularizedFit = lmbda*(norm(V)**2)
fitDAV = normD + matrixFitNormWithoutNormD(D, A, V)
for i in xrange(len(R)):
tensorFit += (normX[i] + fitNormWithoutNormX(X[i], A, R[i]))
fit = 0.5*tensorFit
fit += regularizedFit
fit /= sumNormX
fit += (0.5*fitDAV + extRegularizedFit)/normD
else :
_log.debug('[Algorithm] Preheating is going on.')
toc = time.clock()
exectimes.append( toc - tic )
fitchange = abs(fitold - fit)
_log.debug('[%3d] total fit: %.10f | tensor fit: %.10f | matrix fit: %.10f | delta: %.10f | secs: %.5f' % (iterNum,
fit, tensorFit, fitDAV, fitchange, exectimes[-1]))
fitold = fit
if iterNum > preheatnum and fitchange < conv:
break
return A, R, fit, iterNum+1, array(exectimes), V
def __updateR(X, A, lmbda):
r = A.shape[1]
R = []
At = A.T
if lmbda == 0:
ainv = dot(pinv(dot(At, A)), At)
for i in xrange(len(X)):
R.append( dot(ainv, X[i].dot(ainv.T)) )
else :
AtA = dot(At, A)
tmp = inv(kron(AtA, AtA) + lmbda * eye(r**2))
for i in xrange(len(X)):
AtXA = dot(At, X[i].dot(A))
R.append( dot(AtXA.flatten(), tmp).reshape(r, r) )
return R
def __projectSlices(X, Q):
X2 = []
for i in xrange(len(X)):
X2.append( dot(Q.T, X[i].dot(Q)) )
return X2
parser = argparse.ArgumentParser()
parser.add_argument("--latent", type=int, help="number of latent components", required=True)
parser.add_argument("--lmbda", type=float, help="regularization parameter", required=True)
parser.add_argument("--input", type=str, help="the directory, where the input data are stored", required=True)
parser.add_argument("--outputentities", type=str, help="the file, where the latent embeddings for entities will be output", required=True)
parser.add_argument("--outputterms", type=str, help="the file, where the inverted matrix of latent embeddings for terms will be output", required=True)
parser.add_argument("--outputfactors", type=str, help="the file, where the latent factors will be output", required=True)
parser.add_argument("--log", type=str, help="log file", required=True)
args = parser.parse_args()
numLatentComponents = args.latent
inputDir = args.input
regularizationParam = args.lmbda
outputEntities = args.outputentities
outputTerms = args.outputterms
outputFactors = args.outputfactors
logFile = args.log
logging.basicConfig(filename=logFile, filemode='w', level=logging.DEBUG)
_log = logging.getLogger('EXT-RESCAL')
dim = 0
with open('./%s/entity-ids' % inputDir) as entityIds:
for line in entityIds:
dim += 1
print 'The number of entities: %d' % dim
X = loadX(inputDir, dim)
D = loadD(inputDir, dim)
result = rescal(X, D, numLatentComponents, lmbda=regularizationParam)
print 'Objective function value: %.30f' % result[2]
print '# of iterations: %d' % result[3]
#print the matrices of latent embeddings
A = result[0]
savetxt(outputEntities, A)
V = result[5]
savetxt(outputTerms, V.T)
R = result[1]
with file(outputFactors, 'w') as outfile:
for i in xrange(len(R)):
savetxt(outfile, R[i])