-
Notifications
You must be signed in to change notification settings - Fork 1
/
dssc.m
155 lines (125 loc) · 4.12 KB
/
dssc.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
function [A] = dssc(X,lambda,eta,gamma,type)
% min_{C,A} 1/2||X - XC||_F^2 + eta1/2|||Z|-eta2*A||_F^2 +eta3||Z||_1
% A is a doubly stochastic matrix,diag(Z)=0
% eta1 == lambda, eta2 == eta, eta3 == gamma
[d,n] = size(X);
iter = 0;
t = 0;
maxiter = 1e3;
mu = 1e-6;
maxmu = 1e30;
rho = 1.1;
tol = 1e-4;
e = ones(n,1);
eet = e*e';
I = eye(n);
ttol = 1e-2;
switch type
case 'JDSSC'
tau = 0.001;
Cp = zeros(n,n);
Cn = zeros(n,n);
A = zeros(n,n);
Y = A;
Z = X*(Cp-Cn);
l1 = zeros(n,1);
l2 = zeros(n,1);
L1 = zeros(n,n);
L2 = zeros(d,n);
while iter < maxiter
iter = iter + 1;
%% update Cp,Cn
while t < maxiter
t = t + 1;
Cpt = Cp - tau*(-X'*L2 + mu*X'*(X*(Cp-Cn)-Z));
Cp = 1/(lambda + 1/tau)*(1/tau*Cpt - lambda*Cn + lambda*eta*A -gamma*eet);
Cp = max(Cp,0);
Cp = Cp - diag(diag(Cp));
Cnt = Cn - tau*(X'*L2 - mu*X'*(X*(Cp-Cn)-Z));
Cn = 1/(lambda + 1/tau)*(1/tau*Cnt - lambda*Cp + lambda*eta*A -gamma*eet);
Cn = max(Cn,0);
Cn = Cn - diag(diag(Cn));
if norm(Cp-Cpt,'inf') <= ttol && norm(Cn-Cnt,'inf')<= ttol
% disp('Cp and Cn are updated!')
break;
end
end
%% update A
A = max(1/(lambda*eta^2 + mu)*(lambda*eta*(Cp + Cn) + L1 + mu*Y),0);
%% update Y
P = I - 1/(2*n + 1)*eet;
V = mu*A + 2*mu*eet - e*l1' - l2*e' - L1;
Y = 1/mu*(V - 1/(n+1)*P*V*eet - 1/(n+1)*eet*V*P);
%% update Z
Z = 1/(1+mu)*(X - L2 + mu*X*(Cp - Cn));
leq1 = Y'*e - e;
leq2 = Y*e - e;
leq3 = Y - A;
leq4 = Z - X*(Cp - Cn);
stopC = max([max(max(abs(leq1))),max(max(abs(leq2))),max(max(abs(leq3))),max(max(abs(leq4)))]);
if iter==1 || mod(iter,50)==0 || stopC<tol
disp(['iter ' num2str(iter) ',stopC =' num2str(stopC,'%2.3e')]);
end
if stopC < tol
break;
else
l1 = l1 + mu*leq1;
l2 = l2 + mu*leq2;
L1 = L1 + mu*leq3;
L2 = L2 + mu*leq4;
mu = min(maxmu,mu*rho);
end
end
case 'ADSSC'
Z = elasticnet(X,lambda,gamma);
absZ = abs(Z);
% searching for A by column and row wise which is more efficient
% than the method mentioned in the corresponding reference
Ar = zeros(n,n);
for i=1:n
Ar(i,:) = 1/n*(1 - (sum(absZ(i,:))/eta))*e' + absZ(i,:)/eta;
Ar(i,:) = max(Ar(i,:),0);
end
Ac = zeros(n,n);
for j=1:n
Ac(:,j) = 1/n*(1 - (sum(absZ(:,j))/eta))*e + absZ(:,j)/eta;
Ac(:,j) = max(Ac(:,j),0);
end
A = (Ac + Ar)/2;
end
%% Elastic Net, an algorithm to obtain the initial coefficient matrix for ADSSC
function [Z] = elasticnet(X,eta1,eta3)
% 1/2\|X-XZ\|_F^2 + lambda1/2\|Z\|_F^2 + lambda2\|Z\|_1
% diag(Z)=0
[~,n] = size(X);
iter = 0;
maxiter = 1e4;
mu = 1e-6;
maxmu = 1e30;
rho = 1.1;
tol = 1e-6;
I = eye(n);
XtX = X'*X;
C = zeros(n,n);
Y = zeros(n,n);
while iter < maxiter
iter = iter + 1;
%% update Z
A = XtX + (eta1 + mu)*I;
B = XtX + mu*C - Y;
Z = A\B;
%% update C
temp = Z + Y/mu;
C = max(0,temp - eta3/mu) + min(0,temp + eta3/mu);
leq1 = Z - C;
stopC = max(max(abs(leq1)));
if iter==1 || mod(iter,50)==0 || stopC<tol
disp(['iter ' num2str(iter) ',mu=' num2str(mu,'%2.1e') ',stopALM=' num2str(stopC,'%2.3e')]);
end
if stopC<tol
break;
else
Y = Y + mu*leq1;
mu = min(maxmu,mu*rho);
end
end