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wrapper_stmiss_central.m
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wrapper_stmiss_central.m
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clear;
clc;
addpath('NORST-rmc-master/');
addpath('NORST-rmc-master/PROPACK');
%% Algorithms to run
NORST = 1;
NORST_OFFLINE = 0;
%% Parameter Initialization
n = 1000;
t_max = 3000;
alpha = 60;
f = 100;
MC = 1;
t_calc_pca = [1:alpha: t_max];
t_calc = t_calc_pca;
%NORST
temp_SE_NORST = zeros(length(t_calc_pca), MC);
temp_err_L_NORST = zeros(t_max, MC);
temp_SE_NORST_fed = zeros(length(t_calc_pca), MC);
temp_err_L_NORST_fed = zeros(t_max, MC);
temp_SE_NORST_base = zeros(length(t_calc_pca), MC);
temp_err_L_NORST_base = zeros(t_max, MC);
t_NORST = 0;
err_L_fro_NORST = zeros(MC,1);
for mc = 1 : MC
fprintf('Monte-Carlo iteration %d in progress \n', mc);
%% Generating support set using: a. Moving Object Model b. Bernoulli Model
% a. Moving Object Model
% s = 100;
% S = zeros(n, t_max);
% rho_s = 1;
% b0 = 0.1;
% beta = ceil(b0 * alpha1);
% x_max = 25;
% x_min = 15;
% alpha1 = 100;
% num_changes = floor((t_max -t_train)/beta);
%
% num_changes1 = min(floor(alpha1 / beta), ceil(n/s));
%
% flag = 0;
% ii1 = 1;
% fval1 = 0;
% for ii = 1 : num_changes
% if(~flag) %%downward motion
% if(ii1 <= num_changes1)
% bind = fval1 + (ii1 - 1) * s/rho_s + 1;
% sind = min(bind - 1 + s, n);
% ii1 = ii1 + 1;
% if(ii1 == num_changes1 + 1)
% flag = 1;
% ii1 = 1;
% fval2 = bind;
% end
% end
% else
% if(ii1 <= num_changes1)
% bind = max(fval2 - (ii1 - 1) * s/rho_s , 1);
% sind = bind - 1 + s;
% ii1 = ii1 + 1;
% if(ii1 == num_changes1 + 1)
% flag = 0;
% ii1 = 1;
% end
% end
% end
% idx = bind : sind;
% jdx = (ii-1) * beta + 1 : ii * beta;
% S(idx, jdx) = x_min + ...
% (x_max - x_min) * rand(length(idx), beta);
% T(idx, jdx) = 1;
% end
%
% b. Bernoulli Model
rho = 0.1; % fraction of missing entries
BernMat = rand(n, t_max);
T = 1 .* (BernMat <= 1 - rho); % observed entries' support
%% Generating low-rank matrix
r_0 = 10;
L = zeros(n, t_max);
lambda_min = sqrt(f)/2;
lambda_max = sqrt(f);
offset = 0; %if offset is not zero, eigenvalues (Lambda) are varying in time;
diag_entries1 = offset + [linspace(lambda_max, lambda_min, r_0)];
diag_entries2 = -offset + [linspace(lambda_max, lambda_min, r_0)];
coeff_train = zeros(r_0, t_max);
for cc = 1 : r_0
coeff_train(cc, 1:2:end-1) = -diag_entries1(cc) + ...
2 * diag_entries1(cc) * rand(1, t_max/2);
coeff_train(cc, 2:2:end) = -diag_entries2(cc) + ...
2 * diag_entries2(cc) * rand(1, t_max/2);
end
P = orth(randn(n, r_0));
delta_t = 100;
U0 = P;
subspace_size = 60;
U_track = cell(ceil(t_max/subspace_size),1);
for i=1:length(U_track)
Btemp1 = randn(n);
B1 = (Btemp1 - Btemp1')/2;
t_1 = (i-1)*subspace_size + 1;
t_2 = min(i*subspace_size,t_max);
U_track{i} = U0;
L(:, t_1:t_2) = U0 * coeff_train(:,t_1:t_2);
U = expm(delta_t*B1)*U0;
U0 = U;
end
% P = orth(randn(n, r_0));
% delta_t = 1e-4;
% U0 = P;
% U_track = cell(t_max,1);
% Btemp1 = randn(n);
% B1 = (Btemp1 - Btemp1')/2;
%
% rot_mat = expm(delta_t*B1);
%
% tmp_se = zeros(size(U_track));
% for i=1:length(U_track)
%
%
%
% U_track{i} = U0;
% L(:, i) = U0 * coeff_train(:,i);
% U = rot_mat * U0;
% %tmp_se(i) = Calc_SubspaceError(U, U0);
% U0 = U;
% end
eps_noise = 0; % noise
L = L + eps_noise * (rand(n,t_max) - 0.5);
M = L .* T ;
%% Algorithm parameters for NORST
if(NORST == 1)
fprintf('\tNORST\t');
K = 25;
ev_thresh = 7.5961e-04;
tol = 1e-16;
overlap_step = alpha; % if it is set to alpha then windows don't overlap
R = 0; % number of reuse
P_init = zeros(n,r_0);
% (M,mu,T_obs,P_init,ev_thresh,alpha,K,omega,tol)
t_norst_fed = tic;
[L_hat_fed, S_hat_fed, t_hat_fed, P_track_full_fed] = ...
NORST_nodet(M, T, P_init, ev_thresh, alpha, K, 1, tol);
t_norst_fed = toc(t_norst_fed);
t_norst = tic;
[L_hat, P_hat, S_hat, t_hat, P_track_full, t_calc] = ...
NORST_random(M, T, r_0, ev_thresh, alpha, K,R,overlap_step);
t_NORST = toc(t_norst)
err_L_fro_NORST(mc) = norm(L-L_hat,'fro')/norm(L,'fro');
t_norst_base = tic;
[L_hat_base, S_hat_base, t_hat_base, P_track_full_base] = ...
baseline_PCA(M, T, P_init, ev_thresh, alpha, K, 1, tol);
t_norst_base = toc(t_norst_base);
end
%% Compute Performance Metrics
%frobenius norm errors
if(NORST == 1)
temp_err_L_NORST(:, mc) = sqrt(mean((L - L_hat).^2, 1)) ...
./ sqrt(mean(L.^2, 1));
temp_err_L_NORST_fed(:, mc) = sqrt(mean((L - L_hat_fed).^2, 1)) ...
./ sqrt(mean(L.^2, 1));
end
%subspace errors
for jj = 1 : length(t_calc_pca)
%tt = t_calc_pca(jj);
tt = ceil(t_calc_pca(jj)/subspace_size);
if(NORST == 1)
temp_SE_NORST(jj, mc) = ...
Calc_SubspaceError(P_track_full{jj}, U_track{tt});
temp_SE_NORST_fed(jj, mc) = ...
Calc_SubspaceError(P_track_full_fed{jj}, U_track{tt});
temp_SE_NORST_base(jj, mc) = ...
Calc_SubspaceError(P_track_full_base{jj}, U_track{tt});
end
if(NORST_OFFLINE == 1)
temp_SE_NORST_off(jj, mc) = ...
Calc_SubspaceError(P_track_full{jj}, U_track{tt});
end
end
fprintf('\n')
end
err_SE_NORST = mean(temp_SE_NORST, 2);
err_L_NORST = mean(temp_err_L_NORST, 2);
err_SE_NORST_fed = mean(temp_SE_NORST_fed, 2);
err_L_NORST_fed = mean(temp_err_L_NORST_fed, 2);
err_SE_NORST_base = mean(temp_SE_NORST_base, 2);
err_L_NORST_base = mean(temp_err_L_NORST_base, 2);
figure
strx = 'j';
stry = '$$\log_{10} dist(\hat{P}_{j}, P_{j})$$';
semilogy(t_calc_pca(1:1:end),err_SE_NORST(1:1:end),'-*r','LineWidth',2,'MarkerSize',10);
hold
semilogy(t_calc_pca(1:1:end),err_SE_NORST_fed(1:1:end),'-*b','LineWidth',2,'MarkerSize',10);
semilogy(t_calc_pca(1:1:end),err_SE_NORST_base(1:1:end),'-*k','LineWidth',2,'MarkerSize',10);
grid on
axis tight
xlabel(strx, 'Interpreter', 'LaTeX', 'FontSize', 20);
ylabel(stry, 'Interpreter', 'LaTeX', 'FontSize', 20);
legend('NORST', 'NORST-nodet', 'Baseline-PCA')