-
Notifications
You must be signed in to change notification settings - Fork 114
/
example_low_rank_tensor_models.m
195 lines (158 loc) · 3.96 KB
/
example_low_rank_tensor_models.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
%
% References:
%
% C. Lu. A Library of ADMM for Sparse and Low-rank Optimization. National University of Singapore, June 2016.
% https://github.com/canyilu/LibADMM.
% C. Lu, J. Feng, S. Yan, Z. Lin. A Unified Alternating Direction Method of Multipliers by Majorization
% Minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 40, pp. 527-541, 2018
%
addpath(genpath(cd))
clear
%% Examples for testing the low-rank tensor models
% For detailed description of the sparse models, please refer to the Manual.
opts.mu = 1e-6;
opts.rho = 1.1;
opts.max_iter = 500;
opts.DEBUG = 1;
%% Tensor RRPCA based on sum of nuclear norm minimization (rpca_snn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 5
L = rand(r,r,r);
U1 = rand(n1,r);
U2 = rand(n2,r);
U3 = rand(n3,r);
L = nmodeproduct(L,U1,1);
L = nmodeproduct(L,U2,2);
L = nmodeproduct(L,U3,3); % low rank part
p = 0.05;
m = p*n1*n2*n3;
temp = rand(n1*n2*n3,1);
[~,I] = sort(temp);
I = I(1:m);
Omega = zeros(n1,n2,n3);
Omega(I) = 1;
E = sign(rand(n1,n2,n3)-0.5);
S = Omega.*E; % sparse part, S = P_Omega(E)
Xn = L+S;
lambda = sqrt([max(n1,n2*n3), max(n2,n1*n3), max(n3,n1*n2)]);
lambda = [1 1 1]
[Lhat,Shat,err,iter] = trpca_snn(Xn,lambda,opts);
err
iter
%% low-rank tensor completion based on sum of nuclear norm minimization (lrtc_snn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 5;
X = rand(r,r,r);
U1 = rand(n1,r);
U2 = rand(n2,r);
U3 = rand(n3,r);
X = nmodeproduct(X,U1,1);
X = nmodeproduct(X,U2,2);
X = nmodeproduct(X,U3,3);
p = 0.5;
omega = find(rand(n1*n2*n3,1)<p);
M = zeros(n1,n2,n3);
M(omega) = X(omega);
lambda = [1 1 1];
[Xhat,err,iter] = lrtc_snn(M,omega,lambda,opts);
err
iter
RSE = norm(X(:)-Xhat(:))/norm(X(:))
%% regularized low-rank tensor completion based on sum of nuclear norm minimization (lrtcR_snn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 5;
X = rand(r,r,r);
U1 = rand(n1,r);
U2 = rand(n2,r);
U3 = rand(n3,r);
X = nmodeproduct(X,U1,1);
X = nmodeproduct(X,U2,2);
X = nmodeproduct(X,U3,3);
p = 0.5;
omega = find(rand(n1*n2*n3,1)<p);
M = zeros(n1,n2,n3);
M(omega) = X(omega);
lambda = [1 1 1];
[Xhat,err,iter] = lrtcR_snn(M,omega,lambda,opts);
err
iter
%% Tensor RRPCA based on tensor nuclear norm minimization (rpca_tnn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 0.1*n1 % tubal rank
L1 = randn(n1,r,n3)/n1;
L2 = randn(r,n2,n3)/n2;
L = tprod(L1,L2); % low rank part
p = 0.1;
m = p*n1*n2*n3;
temp = rand(n1*n2*n3,1);
[~,I] = sort(temp);
I = I(1:m);
Omega = zeros(n1,n2,n3);
Omega(I) = 1;
E = sign(rand(n1,n2,n3)-0.5);
S = Omega.*E; % sparse part, S = P_Omega(E)
Xn = L+S;
lambda = 1/sqrt(n3*max(n1,n2));
tic
[Lhat,Shat] = trpca_tnn(Xn,lambda,opts);
RES_L = norm(L(:)-Lhat(:))/norm(L(:))
RES_S = norm(S(:)-Shat(:))/norm(S(:))
trank = tubalrank(Lhat)
%% low-rank tensor completion based on tensor nuclear norm minimization (lrtc_tnn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 0.1*n1 % tubal rank
L1 = randn(n1,r,n3)/n1;
L2 = randn(r,n2,n3)/n2;
X = tprod(L1,L2); % low rank part
p = 0.5;
omega = find(rand(n1*n2*n3,1)<p);
M = zeros(n1,n2,n3);
M(omega) = X(omega);
[Xhat,obj,err,iter] = lrtc_tnn(M,omega,opts);
err
iter
RSE = norm(X(:)-Xhat(:))/norm(X(:))
trank = tubalrank(Xhat)
%% regularized low-rank tensor completion based on tensor nuclear norm minimization (lrtcR_tnn)
n1 = 50;
n2 = n1;
n3 = n1;
r = 0.1*n1 % tubal rank
L1 = randn(n1,r,n3)/n1;
L2 = randn(r,n2,n3)/n2;
X = tprod(L1,L2); % low rank part
p = 0.5;
omega = find(rand(n1*n2*n3,1)<p);
M = zeros(n1,n2,n3);
M(omega) = X(omega);
lambda = 0.5;
[Xhat,Ehat,obj,err,iter] = lrtcR_tnn(M,omega,lambda,opts);
err
iter
%% low-rank tensor recovery from Gaussian measurements based on tensor nuclear norm minimization (lrtr_Gaussian_tnn)
n1 = 30;
n2 = n1;
n3 = 5;
r = 0.2*n1; % tubal rank
X = tprod(randn(n1,r,n3),randn(r,n2,n3)); % size: n1*n2*n3
m = 3*r*(n1+n2-r)*n3+1; % number of measurements
n = n1*n2*n3;
A = randn(m,n)/sqrt(m);
b = A*X(:);
Xsize.n1 = n1;
Xsize.n2 = n2;
Xsize.n3 = n3;
opts.DEBUG = 1;
[Xhat,obj,err,iter] = lrtr_Gaussian_tnn(A,b,Xsize,opts);
RSE = norm(Xhat(:)-X(:))/norm(X(:))
trank = tubalrank(Xhat)