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demo_time_varying.m
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%% DEMO: Adaptive TT for streaming 4-order tensors
clear;clc; close all
run_path;
n_exp = 1;
tt_dim = [10 15 20 1000];
tt_rank = [5 5 5];
fac_noise = 1e-3;
sampling = 1;
outlier_den = 0.1;
outlier_fac = 0;
time_varying = [1e-3, 1e-2, 1e-1];
forget_factor = 0.5;
PER_ATT = zeros(length(time_varying),tt_dim(end));
for ll = 1 : length(time_varying)
time_varying_ll = time_varying(ll);
fprintf('Time-varying %f \n',time_varying_ll);
for ii = 1 : n_exp
fprintf(' run %d/%d \n',ii,n_exp);
%% Generate Data
epsilon = time_varying_ll*ones(1,tt_dim(end));
epsilon(600) = 1; %Aim to create a significant change
[Xtrue,tt_core] = tt_generate_tensor(tt_dim,tt_rank,epsilon);
OPTS_PER.Xtrue = Xtrue;
OPTS_PER.forget_factor = forget_factor;
PER1 = zeros(1,tt_dim(end));
N = fac_noise*randn(tt_dim);
% Outliers
O = zeros(tt_dim(1:end));
NN = prod(tt_dim(1:end));
p = randperm(NN);
L = round(outlier_den * NN);
O(p(1:L)) = outlier_fac * rand(L,1);
% Missing
Omega = rand(tt_dim);
Omega = 1.*(Omega <= sampling);
X_full = Xtrue + O + N;
X_miss = Omega .* X_full;
% Algorithm
[per,~,~] = RATT(X_miss,Omega,tt_rank,OPTS_PER);
PER1 = PER1 + per;
end
PER_ATT(ll,:) = PER1 / n_exp;
end
%% Plot
makerSize = 11;
numbMarkers = 500;
LineWidth = 2;
color = get(groot,'DefaultAxesColorOrder');
red_o = [1,0,0];
blue_o = [0, 0, 1];
mag_o = [1 0 1];
gree_o = [0, 0.5, 0];
black_o = [0.25, 0.25, 0.25];
blue_n = color(1,:);
oran_n = color(2,:);
yell_n = color(3,:);
viol_n = color(4,:);
gree_n = color(5,:);
lblu_n = color(6,:);
brow_n = color(7,:);
lbrow_n = [0.5350 0.580 0.2840];
% %% SEP
T = tt_dim(end);
fig = figure;
hold on;
k = 2;
d1 = semilogy(1:k:T,PER_ATT(1,1:k:end),...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d11 = plot(1:100:T,PER_ATT(1,1:100:end),...
'marker','p','markersize',makerSize,...
'linestyle','none','color',red_o,'LineWidth',LineWidth);
d12 = semilogy(1:1,PER_ATT(1,1:1),...
'marker','p','markersize',makerSize,...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d2 = semilogy(1:k:T,PER_ATT(2,1:k:end),...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
hold on;
d21 = plot(1:100:T,PER_ATT(2,1:100:end),...
'marker','^','markersize',makerSize,...
'linestyle','none','color',blue_o,'LineWidth',LineWidth);
d22 = semilogy(1:1,PER_ATT(2,1:1),...
'marker','^','markersize',makerSize,...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
d3 = semilogy(1:k:T,PER_ATT(3,1:k:end),...
'linestyle','-','color','g','LineWidth',LineWidth);
hold on;
d31 = plot(1:100:T,PER_ATT(3,1:100:end),...
'marker','h','markersize',makerSize,...
'linestyle','none','color','g','LineWidth',LineWidth);
d32 = semilogy(1:1,PER_ATT(3,1:1),...
'marker','h','markersize',makerSize,...
'linestyle','-','color','g','LineWidth',LineWidth);
% d4 = semilogy(1:k:T,PER_ATT(4,1:k:end),...
% 'linestyle','-','color','k','LineWidth',LineWidth);
% hold on;
% d41 = plot(1:100:T,PER_ATT(4,1:100:end),...
% 'marker','p','markersize',makerSize,...
% 'linestyle','none','color','k','LineWidth',LineWidth);
% d42 = semilogy(1:1,PER_ATT(4,1:1),...
% 'marker','p','markersize',makerSize,...
% 'linestyle','-','color','k','LineWidth',LineWidth);
lgd = legend([d12,d22,d32],'$\varepsilon = 10^{-3}$','$ \varepsilon = 10^{-2}$','$\varepsilon = 10^{-1}$');
lgd.FontSize = 18;
set(lgd, 'Interpreter', 'latex', 'Color', [0.95, 0.95, 0.95]);
xlabel('Time Index','interpreter','latex','FontSize',13,'FontName','Times New Roman');
ylabel('RE$(\mathcal{X}_{tr},\mathcal{X}_{es})$','interpreter','latex','FontSize',13,'FontName','Times New Roman');
set(fig, 'units', 'inches', 'position', [0.5 0.5 7.5 6.5]);
h=gca;
set(h,'FontSize',16,'XGrid','on','YGrid','on','GridLineStyle',':','MinorGridLineStyle',':','FontName','Times New Roman');
set(h,'FontSize', 22);
% axis([0 T 1*1e-4 1e1]);
grid on;
set(h, 'YScale', 'log','box','on')