Contents
% An example of nonnegative CP decomposition from partial observations
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 A1 = max(0,randn(N1,R)); A2 = max(0,randn(N2,R)); A3 = max(0,randn(N3,R)); A4 = max(0,randn(N4,R)); % generate tensor M using the above factor matrices M = ktensor({A1,A2,A3,A4}); M = full((arrange(M))); sr = 0.4; % percentage of samples % randomly choose samples known = randsample(N1*N2*N3*N4,round(sr*N1*N2*N3*N4)); data = M.data(known); sn = 60; % signal to noise % -- add noise -- Noise = max(0,randn(size(data))); data = data + 10^(-sn/20)*norm(data)/norm(Noise)*Noise; ndim = [N1,N2,N3,N4];
Solve problem
exact rank works but a rough rank overestimate is also fine
esr = round(1.25*R); % overestimate of rank
opts.tol = 1e-4; opts.maxit = 1000;
t0 = tic;
[A,Out] = ncpc(data,known,ndim,esr,opts);
time = toc(t0);
Iteration: 185
Reporting
relerr = norm(full(A)-M)/norm(M); 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 = 6.85e+000, solution relative error = 4.51e-004
