forked from apache/systemds
-
Notifications
You must be signed in to change notification settings - Fork 0
/
ALS-CG.dml
178 lines (157 loc) · 6.29 KB
/
ALS-CG.dml
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
#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements. See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership. The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied. See the License for the
# specific language governing permissions and limitations
# under the License.
#
#-------------------------------------------------------------
#
# THIS SCRIPT COMPUTES AN APPROXIMATE FACTORIZATION OF A LOW-RANK MATRIX X INTO TWO MATRICES U AND V
# USING THE ALTERNATING-LEAST-SQUARES (ALS) ALGORITHM WITH CONJUGATE GRADIENT.
# MATRICES U AND V ARE COMPUTED BY MINIMIZING A LOSS FUNCTION (WITH REGULARIZATION).
#
# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME TYPE DEFAULT MEANING
# ---------------------------------------------------------------------------------------------
# X String --- Location to read the input matrix X to be factorized
# U String --- Location to write the factor matrix U
# V String --- Location to write the factor matrix V
# rank Int 10 Rank of the factorization
# reg String "L2" Regularization:
# "L2" = L2 regularization;
# "wL2" = weighted L2 regularization
# lambda Double 0.000001 Regularization parameter, no regularization if 0.0
# maxi Int 50 Maximum number of iterations
# check Boolean TRUE Check for convergence after every iteration, i.e., updating U and V once
# thr Double 0.0001 Assuming check is set to TRUE, the algorithm stops and convergence is declared
# if the decrease in loss in any two consecutive iterations falls below this threshold;
# if check is FALSE thr is ignored
# fmt String "text" The output format of the factor matrices L and R, such as "text" or "csv"
# ---------------------------------------------------------------------------------------------
# OUTPUT:
# 1- An m x r matrix U, where r is the factorization rank
# 2- An r x n matrix V
#
# HOW TO INVOKE THIS SCRIPT - EXAMPLE:
# hadoop jar SystemDS.jar -f ALS-CG.dml -nvargs X=INPUT_DIR/X U=OUTPUT_DIR/U V=OUTPUT_DIR/V rank=10 reg="L2" lambda=0.0001 fmt=csv
fileX = $X;
fileU = $U;
fileV = $V;
# Default values of some parameters
r = ifdef($rank, 10);
reg = ifdef($reg, "L2");
lambda = ifdef($lambda, 0.000001);
max_iter = ifdef($maxi, 50);
check = ifdef($check, TRUE);
thr = ifdef($thr, 0.0001);
fmtO = ifdef($fmt, "text");
###### MAIN PART ######
X = read (fileX);
m = nrow (X);
n = ncol (X);
# initializing factor matrices
U = rand (rows = m, cols = r, min = -0.5, max = 0.5); # mxr
V = rand (rows = n, cols = r, min = -0.5, max = 0.5); # nxr
W = (X != 0);
# check for regularization
row_nonzeros = matrix(0,rows=1,cols=1);
col_nonzeros = matrix(0,rows=1,cols=1);
if( reg == "L2" ) {
print ("BEGIN ALS-CG SCRIPT WITH NONZERO SQUARED LOSS + L2 WITH LAMBDA - " + lambda);
row_nonzeros = matrix(1, nrow(W), 1);
col_nonzeros = matrix(1, ncol(W), 1);
}
else if( reg == "wL2" ) {
print ("BEGIN ALS-CG SCRIPT WITH NONZERO SQUARED LOSS + WEIGHTED L2 WITH LAMBDA - " + lambda);
row_nonzeros = rowSums(W);
col_nonzeros = t(colSums(W));
}
else {
stop ("wrong regularization! " + reg);
}
# Loss Function with L2:
# f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
# + 0.5 * lambda * (sum (U ^ 2) + sum (V ^ 2))
# Loss Function with weighted L2:
# f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
# + 0.5 * lambda * (sum (U ^ 2 * row_nonzeros) + sum (V ^ 2 * col_nonzeros))
is_U = TRUE; # TRUE = Optimize U, FALSE = Optimize V
maxinneriter = r ; # min (ncol (U), 15);
loss_init = 0.0; # only used if check is TRUE
if( check ) {
loss_init = 0.5 * sum( (X != 0) * (U %*% t(V) - X) ^ 2);
loss_init = loss_init + 0.5 * lambda * (sum (U ^ 2 * row_nonzeros) + sum (V ^ 2 * col_nonzeros));
print ("----- Initial train loss: " + loss_init + " -----");
}
it = 0;
converged = FALSE;
while( as.integer(it/2) < max_iter & ! converged )
{
it = it + 1;
if( is_U ) {
G = ((X != 0) * (U %*% t(V) - X)) %*% V + lambda * U * row_nonzeros;
}
else {
G = t(t(U) %*% ((X != 0) * (U %*% t(V) - X))) + lambda * V * col_nonzeros;
}
R = -G;
S = R;
norm_G2 = sum (G ^ 2);
norm_R2 = norm_G2;
inneriter = 1;
tt = 0.000000001;
while( norm_R2 > tt * norm_G2 & inneriter <= maxinneriter )
{
if( is_U ) {
HS = (W * (S %*% t(V))) %*% V + lambda * S * row_nonzeros;
alpha = norm_R2 / sum (S * HS);
U = U + alpha * S; # OK since U is not used in HS
}
else {
HS = t(t(U) %*% (W * (U %*% t(S)))) + lambda * S * col_nonzeros;
alpha = norm_R2 / sum (S * HS);
V = V + alpha * S; # OK since V is not used in HS
}
R = R - alpha * HS;
old_norm_R2 = norm_R2;
norm_R2 = sum (R ^ 2);
S = R + (norm_R2 / old_norm_R2) * S;
inneriter = inneriter + 1;
}
is_U = ! is_U;
# check for convergence
if( check & (it%%2 == 0) ) {
loss_cur = 0.5 * sum( (X != 0) * (U %*% t(V) - X) ^ 2);
loss_cur = loss_cur + 0.5 * lambda * (sum (U ^ 2 * row_nonzeros) + sum (V ^ 2 * col_nonzeros));
loss_dec = (loss_init - loss_cur) / loss_init;
print ("Train loss at iteration (" + as.integer(it/2) + "): " + loss_cur + " loss-dec " + loss_dec);
if( loss_dec >= 0 & loss_dec < thr | loss_init == 0 ) {
print ("----- ALS-CG converged after " + as.integer(it/2) + " iterations!");
converged = TRUE;
}
loss_init = loss_cur;
}
}
if( check ) {
print ("----- Final train loss: " + loss_init + " -----");
}
if( !converged ) {
print ("Max iteration achieved but not converged!");
}
V = t(V);
write (U, fileU, format=fmtO);
write (V, fileV, format=fmtO);