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demo_p_alpha.m
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% Effect of parameters alpha and p on performance of aFAPI
clear;clc; close all
addpath(genpath('subspace_trackers\'))
%% Parameters
n = 50;
r = 5;
T = 1001;
time_varying_factor = 1e-3*ones(1,T);
beta = 0.99; % forgetting factor
alpha = [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99] ; % alpha-divergence
lp = [1 1.25 1.5 1.75 2];
% Generating data
% true data
disp('+ Data Generating ...')
[X,U_tr] = data_generator(n,T,r,time_varying_factor);
% noise
fac_noise = 1;
epsilon = 0.2; % for non-gaussian noise
sigma_n = 10;
mu_n = 10;
Noise = (1-epsilon)*randn(n,T) + epsilon*(randn(n,T));
outlier_1 = (1-epsilon)*randn(n,1) + epsilon*0.5*sigma_n*(randn(n,1) + mu_n);
outlier_2 = (1-epsilon)*randn(n,1) + epsilon*sigma_n*(randn(n,1) + mu_n);
outlier_3 = (1-epsilon)*randn(n,1) + epsilon*2*sigma_n*(randn(n,1) + mu_n);
Noise(:,400) = outlier_2;
Noise(:,600) = outlier_3;
Noise(:,800) = outlier_3;
X_noise = X + Noise;
disp('+ Processing ...')
idx = 1;
for ii = 1 : length(alpha)
for jj = 1 : length(lp)
fprintf('+ Case %d: (alpha = %0.1f | lp = %0.1f) \n',idx,alpha(ii),lp(jj))
[~, eta_RFAPI_ii,rho_RFAPI_ii] = alpha_FAPI(X_noise,beta,alpha(ii),U_tr,lp(jj));
eta_RFAPI{ii,jj} = eta_RFAPI_ii;
rho_RFAPI{ii,jj} = rho_RFAPI_ii;
idx = idx + 1;
end
end
%% PLOT
disp('Plotting ....')
fig1 = figure; hold on;
for ii = 1:7
semilogy(eta_RFAPI{ii,5},'LineWidth',1.5);
end
semilogy(eta_RFAPI{8,5},'-b','LineWidth',2);
semilogy(eta_RFAPI{9,5},'-g','LineWidth',2);
semilogy(eta_RFAPI{10,5},'-r','LineWidth',2);
axis([0 1000 1e-3 10 ]);
leg = legend('$\alpha=0.1$','$\alpha=0.2$','$\alpha=0.3$','$\alpha=0.4$','$\alpha=0.5$', ...
'$\alpha=0.6$','$\alpha=0.7$','$\alpha=0.8$','$\alpha=0.9$','$\alpha=0.99$')
set(leg,'interpreter','latex');
title('p = 2 (standard)')
ylabel('SEP','interpreter','latex','FontSize',13,'FontName','Times New Roman');
xlabel('Data Samples','interpreter','latex','FontSize',13,'FontName','Times New Roman');
h=gca;
set(gca, 'YScale', 'log','FontSize',24)
set(h,'FontSize',24,'XGrid','on','YGrid','on','FontName','Times New Roman');
set(h,'Xtick',0:200:T,'FontSize',24,'XGrid','on','YGrid','on','FontName','Times New Roman');
grid on;
box on;
set(fig1, 'units', 'inches', 'position', [0.5 0.5 9 7]);
fig2 = figure; hold on;
for ii = 1:5
semilogy(eta_RFAPI{7,ii},'LineWidth',1.5);
end
axis([0 1000 1e-3 10 ]);
ylabel('SEP','interpreter','latex','FontSize',13,'FontName','Times New Roman');
xlabel('Data Samples','interpreter','latex','FontSize',13,'FontName','Times New Roman');
h=gca;
set(gca, 'YScale', 'log','FontSize',24)
set(h,'FontSize',24,'XGrid','on','YGrid','on','FontName','Times New Roman');
set(h,'Xtick',0:200:T,'FontSize',24,'XGrid','on','YGrid','on','FontName','Times New Roman');
grid on;
box on;
set(fig2, 'units', 'inches', 'position', [0.5 0.5 9 7]);
leg2 = legend('$p=1$','$p=1.25$','$p=1.5$','$p=1.75$','$p=2$');
set(leg2,'interpreter','latex');
title('$\alpha = 0.7$','interpreter','latex')