Contents

% An example of nonnegative CP decomposition

Generate synthetic 4-order tensor

rand('seed',0); randn('seed',0);
N1 = 30; N2 = 30; N3 = 30; N4 = 30; % tensor dimension
R=10; % tensor rank

% randomly generate factor matrices
A_org = max(0,randn(N1,R));
B_org = max(0,randn(N2,R));
C_org = max(0,randn(N3,R));
D_org = max(0,randn(N4,R));

% get tensor M using the above factor matrices
M = ktensor({A_org,B_org,C_org,D_org});
M = arrange(M);
Mtrue = full(ktensor(M));

sn = 60; % signal to noise ratio
% -- add noise --
N = tensor(max(0,randn(N1,N2,N3,N4)));
M = Mtrue + 10^(-sn/20) * norm(Mtrue)*N/norm(N);

Solve problem

opts.maxit = 1000; % max number of iterations
opts.tol = 1e-4; % stopping tolerance
t0 = tic;
[A,Out] = ncp(M,R,opts);
time = toc(t0);

Iteration:   84

Reporting

relerr = norm(full(A)-Mtrue)/norm(Mtrue);
fprintf('time = %4.2e, ',time);
fprintf('solution relative error = %4.2e\n\n',relerr);

figure;
semilogy(1:Out.iter, Out.hist_obj,'k-','linewidth',2);
xlabel('iteration','fontsize',12);
ylabel('objective value','fontsize',12)

figure;
semilogy(1:Out.iter, Out.hist_rel(2,:),'k-','linewidth',2);
xlabel('iteration','fontsize',12);
ylabel('relative residual','fontsize',12)

time = 9.65e-001, solution relative error = 4.26e-004

Download this m-file

Published with MATLAB® 7.13