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stmiss_fed_sigvar.m
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stmiss_fed_sigvar.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 = 50;
t_calc_pca = [1:alpha: t_max];
t_calc = t_calc_pca;
sigrange = [1, 1e-2, 1e-4, 1e-6];
%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), length(sigrange), MC);
temp_err_L_NORST_fed = zeros(t_max, length(sigrange), MC);
t_NORST = 0;
err_L_fro_NORST = zeros(MC,1);
for mc = 1 : MC
sigcount = 1;
for sigma_iter = sigrange
fprintf('Monte-Carlo iteration %d, sigma %.0e in progress \n', mc, sigma_iter);
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 = 30;
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 = 1500;
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
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);
t_norst_fed = tic;
[L_hat_fed, P_hat_fed, S_hat_fed, t_hat_fed, P_track_full_fed, t_calc_fed] = ...
NORST_fed_new(M, T, r_0, ev_thresh, alpha, K,R,overlap_step, sigma_iter);
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');
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(:, sigcount, 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 = 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, sigcount, mc) = ...
Calc_SubspaceError(P_track_full_fed{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
sigcount = sigcount + 1;
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, 3);
err_L_NORST_fed = mean(temp_err_L_NORST_fed, 3);
figure
strx = 't';
stry = '$$\log_{10} dist(\hat{P}_{(t)}, P_{(t)})$$';
semilogy(t_calc_pca(1:2:end),err_SE_NORST_fed(1:2:end, 1),'-*r','LineWidth',2,'MarkerSize',10);
hold
semilogy(t_calc_pca(1:2:end),err_SE_NORST_fed(1:2:end, 2),'-*k','LineWidth',2,'MarkerSize',10);
semilogy(t_calc_pca(1:2:end),err_SE_NORST_fed(1:2:end, 3),'-*b','LineWidth',2,'MarkerSize',10);
semilogy(t_calc_pca(1:2:end),err_SE_NORST_fed(1:2:end, 4),'-*g','LineWidth',2,'MarkerSize',10);
grid on
axis tight
xlabel(strx, 'Interpreter', 'LaTeX', 'FontSize', 20);
ylabel(stry, 'Interpreter', 'LaTeX', 'FontSize', 20);
legend('sig1', 'sig2', 'sig3', 'sig4')