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demo_ACP_time_varying_factor.m
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demo_ACP_time_varying_factor.m
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%% This demo illustrates the tracking ability of ACP in time-varying environments
clc; clear all; close all;
run_path;
n_exp = 3; % Number of independent runs
fac_noise = 1e-4; % Noise factor
sampling = 0.9; % (1-sampling) = missing density
tensor_dim = [20 20 20 1000]; % Tensor Dimension
R = 5; % CP rank
Mag = [1e-1 1e-2 1e-3 1e-4]; % time-varying factor
PER_ACP = cell(length(Mag),1);
for m = 1 : length(Mag)
PER_ACP{m,1} = zeros(length(tensor_dim),tensor_dim(end));
end
%% Main Program
N = length(tensor_dim);
for m = 1 : length(Mag);
mag = Mag(m);
fprintf('\n Time-varying factor %f: \n',mag);
epsilon = mag*ones(1,tensor_dim(end));
epsilon(600) = 1;
PER_Our = zeros(length(tensor_dim),tensor_dim(end));
for ii = 1 : n_exp
fprintf(' + Run [%d/%d]: \n', ii, n_exp)
%% Generate True Tensor
Factor = cell(1,N);
for n = 1 : N
Factor{1,n} = randn(tensor_dim(n),R);
end
% True Data
Size_Fixed = tensor_dim(1:end-1);
Num_Slides = tensor_dim(end);
X_stream = cp_online_generator(Size_Fixed,R,Num_Slides,epsilon);
OPTS.Factor_True = X_stream(:,2);
OPTS.Slide_True = X_stream(:,1);
% Add Missing + Gaussian Noise
X_cell = cell(tensor_dim(end),1);
Omega = cell(tensor_dim(end),1);
for t = 1 : tensor_dim(end)
Omega_t = rand(tensor_dim(1:end-1));
Omega_t = 1 .* (Omega_t <= sampling);
Omega{t,1} = Omega_t;
X_cell{t,1} = OPTS.Slide_True{t,1} + fac_noise * randn(tensor_dim(1:end-1));
X_cell{t,1} = Omega_t .* X_cell{t,1};
end
%% Our Method
t_start = tic;
[~,PER] = ACP(X_cell,Omega,R,OPTS);
t_end = toc(t_start);
PER_Our = PER_Our + PER;
end
PER_Our = PER_Our/n_exp;
PER_ACP{m,1} = PER_Our;
end
% For four values of time-varying factor
PER_Our1 = PER_ACP{1,1};
PER_Our2 = PER_ACP{2,1};
PER_Our3 = PER_ACP{3,1};
PER_Our4 = PER_ACP{4,1};
%% PLOT RESULTS
makerSize = 14;
numbMarkers = 50;
LineWidth = 2;
set(0, 'defaultTextInterpreter', 'latex');
color = get(groot,'DefaultAxesColorOrder');
red_o = [1,0,0];
blue_o = [0, 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];
%%
fig = figure;
hold on;
k = 1;
K = tensor_dim(end);
d1 = semilogy(1:k:K,PER_Our1(3,1:k:end),...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d11 = plot(1:100:K,PER_Our1(3,1:100:end),...
'marker','d','markersize',makerSize,...
'linestyle','none','color',red_o,'LineWidth',LineWidth);
d12 = semilogy(1:1,PER_Our1(3,1),...
'marker','d','markersize',makerSize,...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d2 = semilogy(1:k:K,PER_Our2(3,1:k:end),...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
d21 = plot(1:100:K,PER_Our2(3,1:100:end),...
'marker','o','markersize',makerSize,...
'linestyle','none','color',blue_o,'LineWidth',LineWidth);
d22 = semilogy(1:1,PER_Our2(3,1),...
'marker','o','markersize',makerSize,...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
d3 = semilogy(1:k:K,PER_Our3(3,1:k:end),...
'linestyle','-','color',gree_o,'LineWidth',LineWidth);
% 'marker','d','markersize',makerSize,'markerfacecolor','w',...
d31 = plot(1:100:K,PER_Our3(3,1:100:end),...
'marker','s','markersize',makerSize,...
'linestyle','none','color',gree_o,'LineWidth',LineWidth);
d32 = semilogy(1:1,PER_Our3(3,1:1),...
'marker','s','markersize',makerSize,...
'linestyle','-','color',gree_o,'LineWidth',LineWidth);
d4 = semilogy(1:k:K,PER_Our4(3,1:k:end),...
'linestyle','-','color',viol_n,'LineWidth',LineWidth);
% 'marker','d','markersize',makerSize,'markerfacecolor','w',...
d41 = plot(1:100:K,PER_Our4(3,1:100:end),...
'marker','p','markersize',makerSize,...
'linestyle','none','color',viol_n,'LineWidth',LineWidth);
d42 = semilogy(1:1,PER_Our4(3,1:1),...
'marker','p','markersize',makerSize,...
'linestyle','-','color',viol_n,'LineWidth',LineWidth);
lgd = legend([d12 d22 d32 d42],'$\epsilon = 10^{-1}$','$\epsilon = 10^{-2}$','$\epsilon = 10^{-3}$','$\epsilon = 10^{-4}$');
lgd.FontSize = 22;
set(lgd, 'Interpreter', 'latex', 'Color', [0.95, 0.95, 0.95]);
xlabel('Time Index - $t$','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 8 7]);
h=gca;
set(gca, 'YScale', 'log')
set(h,'Xtick',0:200:K,'FontSize',24,'XGrid','on','YGrid','on','GridLineStyle',':','MinorGridLineStyle','none',...
'FontName','Times New Roman');
axis([0 K 5e-5 1e1]);
grid on;
box on;
set(fig, 'units', 'inches', 'position', [0.5 0.5 8 7]);
%%
fig2 = figure;
hold on;
k = 1;
K = tensor_dim(end);
d1 = semilogy(1:k:K,PER_Our1(1,1:k:end),...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d11 = plot(1:100:K,PER_Our1(1,1:100:end),...
'marker','d','markersize',makerSize,...
'linestyle','none','color',red_o,'LineWidth',LineWidth);
d12 = semilogy(1:1,PER_Our1(1,1),...
'marker','d','markersize',makerSize,...
'linestyle','-','color',red_o,'LineWidth',LineWidth);
d2 = semilogy(1:k:K,PER_Our2(1,1:k:end),...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
d21 = plot(1:100:K,PER_Our2(1,1:100:end),...
'marker','o','markersize',makerSize,...
'linestyle','none','color',blue_o,'LineWidth',LineWidth);
d22 = semilogy(1:1,PER_Our2(1,1),...
'marker','o','markersize',makerSize,...
'linestyle','-','color',blue_o,'LineWidth',LineWidth);
d3 = semilogy(1:k:K,PER_Our3(1,1:k:end),...
'linestyle','-','color',gree_o,'LineWidth',LineWidth);
% 'marker','d','markersize',makerSize,'markerfacecolor','w',...
d31 = plot(1:100:K,PER_Our3(1,1:100:end),...
'marker','s','markersize',makerSize,...
'linestyle','none','color',gree_o,'LineWidth',LineWidth);
d32 = semilogy(1:1,PER_Our3(1,1:1),...
'marker','s','markersize',makerSize,...
'linestyle','-','color',gree_o,'LineWidth',LineWidth);
d4 = semilogy(1:k:K,PER_Our4(1,1:k:end),...
'linestyle','-','color',viol_n,'LineWidth',LineWidth);
% 'marker','d','markersize',makerSize,'markerfacecolor','w',...
d41 = plot(1:100:K,PER_Our4(1,1:100:end),...
'marker','p','markersize',makerSize,...
'linestyle','none','color',viol_n,'LineWidth',LineWidth);
d42 = semilogy(1:1,PER_Our4(1,1:1),...
'marker','p','markersize',makerSize,...
'linestyle','-','color',viol_n,'LineWidth',LineWidth);
lgd = legend([d12 d22 d32 d42],'$\epsilon = 10^{-1}$','$\epsilon = 10^{-2}$','$\epsilon = 10^{-3}$','$\epsilon = 10^{-4}$');
lgd.FontSize = 22;
set(lgd, 'Interpreter', 'latex', 'Color', [0.95, 0.95, 0.95]);
xlabel('Time Index - $t$','interpreter','latex','FontSize',13,'FontName','Times New Roman');
ylabel('RE $(\mathbf{U}_{tr}, \mathbf{U}_{es})$','interpreter','latex','FontSize',13,'FontName','Times New Roman');
set(fig2, 'units', 'inches', 'position', [0.5 0.5 8 7]);
h=gca;
set(gca, 'YScale', 'log')
set(h,'Xtick',0:200:K,'FontSize',24,'XGrid','on','YGrid','on','GridLineStyle',':','MinorGridLineStyle','none',...
'FontName','Times New Roman');
axis([0 K 5e-5 1e1]);
grid on;
box on;
set(fig2, 'units', 'inches', 'position', [0.5 0.5 8 7]);