-
Notifications
You must be signed in to change notification settings - Fork 0
/
cpnonneg_als.m
199 lines (158 loc) · 4.55 KB
/
cpnonneg_als.m
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
function [U lambda]= cpnonneg_als(X,R,constrain_dim,update_order,quiet,init_method,tol)
% my_cp_als - CP decomposition with ALS
% some dimension can be constrained to be nonnegtive
%
%
% Syntax: U = my_cp_als(X,R,constrain_dim)
%
% Inputs:
% X - tensor, a multiway array
% R - estimated rank
% constrain_dim - the dimension index constrained to be nonnegative
% update_order - the order to update
% quiet - true: no display; false: display
% init_method - 1: random vector; 2: leading eigenvalues of Xn*Xn'
%
% Outputs:
% U - a structure contains decomposed array
% Example:
% tt1 = randn(2,3);
% tt2 = randn(3,3);
% tt3 = rand(4,3);
% test_tensor = zeros(2,3,4);
% for i = 1:3
% temp1 = tt1(:,i)*tt2(:,i)';
% for j = 1:4
% test_tensor(:,:,j) = test_tensor(:,:,j) + temp1*tt3(j,i);
% end
% end
% U = my_cp_als(test_tensor,3,1);
% Other m-files required:
% Subfunctions: none
% MAT-files required: tensor toolbox(http://www.sandia.gov/~tgkolda/TensorToolbox/index-2.5.html)
%
% See also: cp_als
% Author: Chaohua Wu
% Department of Biomedical Engineering, Tsinghua University
% email: xs.wuchaohua@outlook.com
% Dec 21 2014; revision:
%------------- BEGIN CODE --------------
if nargin < 1
tt1 = randn(6,3);
tt2 = randn(7,3);
tt3 = rand(8,3);
test_tensor = zeros(6,7,8);
for i = 1:3
temp1 = tt1(:,i)*tt2(:,i)';
for j = 1:size(test_tensor,3)
test_tensor(:,:,j) = test_tensor(:,:,j) + temp1*tt3(j,i);
end
end
X = test_tensor;
R = 3;
constrain_dim = 3;
update_order = [1 2 3];
quiet = false;
init_method = 1;
tol = 10^-4;
end
dims = size(X);
n_dim = length(dims);
U = cell(n_dim,1);
if (constrain_dim > n_dim) || (constrain_dim < 1)
constrain_dim = 0;
end
for i = 1:n_dim
if init_method == 1
if i ~= constrain_dim
U{i} = randn(dims(i), R);
else
U{i} = rand(dims(i), R);
end
end
if init_method == 2
matrix_init = my_matricization(X,i);
[U{i},~] = eigs(matrix_init*matrix_init',R);
end
end
deltaU = 1;
iter = 0;
while deltaU > tol
U_old = U;
for i = update_order(1:n_dim)
temp_matrix = my_matricization(X,i);
[dimseq_without_i,~] = dimseq(n_dim,i);
dimseq_without_i = dimseq_without_i(end:-1:1);
P = khatrirao(U{dimseq_without_i});
if i ~= constrain_dim
Unew = P\temp_matrix';
U{i} = Unew';
I = sum(abs(U{i}),1) == 0;
if sum(I) ~= 0
disp('warning: there is zero loading')
U{i}(:,I) = 10^-5;
end
else
%%%%%%%%%%% nonnegtive constrianed least square
temp_matrix = temp_matrix';
num_i = size(temp_matrix,2);
temp_U_i = zeros(size(U{i}))';
for j = 1:num_i
temp_U_i(:,j) = lsqnonneg(P,temp_matrix(:,j));
end
U{i} = temp_U_i';
I = sum(abs(U{i}),1) == 0;
if sum(I) ~= 0
disp('warning: there is zero loading')
U{i}(:,I) = 10^-5;
end
end
end
deltaU = diffU(U,U_old);
iter = iter+1;
if ~quiet
disp(['iteration number ',num2str(iter),' deltaU = ',num2str(deltaU)]);
end
end
if quiet
disp(['iteration number ',num2str(iter),' deltaU = ',num2str(deltaU)]);
end
lambda = ones(R,1);
for i = 1:R
for j = 1: n_dim
temp = std(U{j}(:,i));
lambda(i) = lambda(i)*temp;
U{j}(:,i) = U{j}(:,i)/temp;
end
end
end
function flatten_matrix = my_matricization(X,md)
dims = size(X);
n_dim = length(dims);
if (md <0) || (md > n_dim)
error('the dimension to matricization does not exsit');
end
[dimseq_without_i,dimseq_first_i] = dimseq(n_dim,md);
flatten_matrix = permute(X,dimseq_first_i);
flatten_matrix = reshape(flatten_matrix, dims(md),prod(dims(dimseq_without_i)));
end
function [dimseq_without_i,dimseq_first_i] = dimseq(n_dim,i)
if i == 1
dimseq_without_i = [i+1:n_dim];
dimseq_first_i = [1:n_dim];
else if i == n_dim
dimseq_without_i = [1:i-1];
dimseq_first_i = [i,1:i-1];
else
dimseq_without_i = [1:i-1,i+1:n_dim];
dimseq_first_i = [i,1:i-1,i+1:n_dim];
end
end
end
function deltaU = diffU(U,U_old)
n = length(U);
deltaU = 0;
for i = 1:n
deltaU = norm(U{i}-U_old{i},'fro')/norm(U{i},'fro') + deltaU;
end
end