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inc_windowed_DMD_ERP.m
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inc_windowed_DMD_ERP.m
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clc
clearvars
close all
resultdir_all='Results';
if (~exist(resultdir_all,'dir'))
mkdir(resultdir_all);
end
figures_resultdir_all=strcat(resultdir_all,'\Figures');
if (~exist(figures_resultdir_all,'dir'))
mkdir(figures_resultdir_all);
end
mat_resultdir_all=strcat(resultdir_all,'\mat files');
if (~exist(mat_resultdir_all,'dir'))
mkdir(mat_resultdir_all);
end
ERP_Recon_figures=strcat(figures_resultdir_all,'\ERP Reconstruction');
if (~exist(ERP_Recon_figures,'dir'))
mkdir(ERP_Recon_figures);
end
ERP_Pred_figures=strcat(figures_resultdir_all,'\ERP Prediction');
if (~exist(ERP_Pred_figures,'dir'))
mkdir(ERP_Pred_figures);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Threshold Levels
thresh_vec=[0.01 0.001];threshold_label={''};thresh_str_vec={''};
for thr_idx=1:length(thresh_vec)
thresh_str_vec{thr_idx}=strcat('th',num2str(thr_idx));
threshold_label{thr_idx}=num2str(thresh_vec(thr_idx));
end
FS=512;dt=1/FS;initail_pre_event_time=1;
wind=floor(initail_pre_event_time*FS);future_pred_samples=FS/8;
elec_FCz_num=47;
data_event_str={'correcteeg_BPF_110','erroneouseeg_BPF_110'};
event_name={'Correct','Erroneous'};
reg_data_dir=strcat('processed data\');
for event_idx1=1:2
eegcarhpfsetfile=strcat(reg_data_dir,data_event_str{event_idx1},'.mat');
for thr_idx1=1:length(thresh_vec)
thresh=thresh_vec(thr_idx1);
fprintf('loading data for %s events.... \n',event_name{event_idx1});
EEG=matfile(eegcarhpfsetfile);
Data=EEG.ERP;Time=EEG.time;
test_time_f=0.40;
[~,erp_ind_f]=min(abs(Time-test_time_f));erp_ind_f=erp_ind_f+wind;
test_time_0=0.20;
[~,erp_ind_0]=min(abs(Time-test_time_0));erp_ind_0=erp_ind_0+wind;
Datax=Data(:,1:end-1);
Datay=Data(:,2:end);
[n_data,m_data]=size(Datax);
Data_x_wind=Datax(:,1:wind);Data_y_wind=Datay(:,1:wind);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Initial DMD model
[U1,Seg1,V1]=svd(Data_x_wind);Seg10=(diag(Seg1))';
Dataxhat(:,1:wind)=U1*Seg1*V1';
rtil1 = length(find(diag(Seg1)>=thresh));
Uo=U1;Vo=V1;Sego=Seg1;rtilo=rtil1;
Ux=Uo(:,1:rtilo);Segx=Sego(1:rtilo,1:rtilo);Vx= Vo(:,1:rtilo);
A0=Data_y_wind*Vx*(eye(size(Segx))/Segx)*Ux';
Ar10=A0;
err_rms_pred=zeros(length(1:m_data-wind),1);
err_time_pred=zeros(length(1:m_data-wind),1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Incremental Weighted DMD
for sample_idx=1:erp_ind_f-wind
fprintf('===========================================\n');
fprintf('iteration # %d out of %d .... \n',sample_idx,erp_ind_f-wind);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Windowed Incremental SVD Update
%%% Removing x(k-w+1)
Vi=Vo;Ui=Uo;Segi=Sego;
xd=Datax(:,sample_idx);
px=Ui'*xd;
[nv,~]=size(Vi);zd=[1;zeros(nv-1,1)];
pz=Vi'*zd;
Sd0=Segi-px*pz';
[Ud1,Segd1,Vd1]=svd(Sd0);
Vd2=Vi*Vd1;
Segd2=Segd1;
Ud2=Ui*Ud1;
Data_xdhat_wind=Ud2*Segd2*Vd2';
Data_xd_wind=[zeros(n_data,1) Datax(:,sample_idx+1:wind+sample_idx-1)];
Uo=Ud2;Vo=Vd2;Sego=Segd2;
%%% Adding x(k+1)
Vi=Vo;Ui=Uo;Segi=Sego;
xu=Datax(:,sample_idx+wind);
px=Ui'*xu;qx=xu-Ui*px;
rx=norm(qx);qx=qx./rx;
[nv,mv]=size(Vi);zu=[zeros(nv,1);1];
pz=[Vi;zeros(1,mv)]'*zu;
qz=zu-[Vi;zeros(1,mv)]*pz;
rz=norm(qz);qz=qz./rz;
Su0=[Segi , px*rz];
[Uu1,Segu1,Vu1]=svd(Su0);
Vu2=[[Vi;zeros(1,mv)] qz]*Vu1;
Uu2=Ui*Uu1;
Segu2=Segu1;
Uo=Uu2;
Vo=Vu2(2:end,1:wind);Sego=Segu2(:,1:wind);
Data_xu_hat=Uo*Sego*Vo';
Data_xu_wind=Datax(:,sample_idx+1:wind+sample_idx);
rtilo = length(find(diag(Seg1)>=thresh)); Ux=Uo(:,1:rtilo);Vx= Vo(:,1:rtilo);
Segx=Sego(1:rtilo,1:rtilo);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Windowed Incremental DMD Model Update
vs_telda=Vo(end,1:rtilo);Segx_inv=(eye(rtilo)/Segx);
yu=Datay(:,sample_idx+wind);
err1=(yu-Ar10*xu);
Ar11=Ar10 +err1*vs_telda* Segx_inv*Ux';
Ar10=Ar11;
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Reduced Dimention DMD model
A=Ux'*Ar10*Ux;[W_telda,D_telda]=eig(A);lambda_telda=diag(D_telda);
omega_telda=log(lambda_telda)/dt;
phi=Ux*W_telda;
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%ERP Prediction
if (sample_idx+wind==erp_ind_0)
x1=Datax(:,erp_ind_0-1);b= pinv(phi)*x1;time=(1:erp_ind_f-erp_ind_0+1)./FS;
time_dynamics=zeros(length(b),length(time));
for iter=1:length(time)
time_dynamics(:,iter)=(b.*exp(omega_telda*time(iter)));
end
erp_hat=real(phi*time_dynamics);
R_y=max(Datay(elec_FCz_num,erp_ind_0:erp_ind_f))-min(Datay(elec_FCz_num,erp_ind_0:erp_ind_f));
erp_pred_rms=(rms(erp_hat(elec_FCz_num,:)-Datay(elec_FCz_num,erp_ind_0:erp_ind_f)))/R_y;
eeg_hat_best=erp_hat(elec_FCz_num,:);
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).rms_erp_pred=erp_pred_rms;
x1=Datax(:,wind);b= pinv(phi)*x1;time=(1:erp_ind_f-wind)./FS;
time_dynamics=zeros(length(b),length(time));
for iter=1:length(time)
time_dynamics(:,iter)=(b.*exp(omega_telda*time(iter)));
end
erp_hat=real(phi*time_dynamics); erp_hat=erp_hat(elec_FCz_num,:);
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).erp_pred=erp_hat';
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).time_pred=time;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%ERP Reconstruction
x1=Datax(:,wind);b= pinv(phi)*x1;time=(1:erp_ind_f-wind)./FS;
time_dynamics=zeros(length(b),length(time));
for iter=1:length(time)
time_dynamics(:,iter)=(b.*exp(omega_telda*time(iter)));
end
erp_hat=real(phi*time_dynamics);
eeg_recon=erp_hat(elec_FCz_num,:);
time_recon=time;
R_y=max(Datay(elec_FCz_num,erp_ind_0:erp_ind_f))-min(Datay(elec_FCz_num,erp_ind_0:erp_ind_f));
err_rms_recon=(rms(erp_hat(elec_FCz_num,erp_ind_0-wind:erp_ind_f-wind)-Datay(elec_FCz_num,erp_ind_0:erp_ind_f)))/R_y;
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).erp_recon=erp_hat(elec_FCz_num,:);
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).time_recon=time_recon;
dynamics_windowed_inc.(event_name{event_idx1}).(thresh_str_vec{thr_idx1}).rms_erp_recon=err_rms_recon;
end
dynamics_windowed_inc.(event_name{event_idx1}).eegdata_rec=Datay(elec_FCz_num,wind+1:erp_ind_f);
end
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Plotting Predicted ERP
close all
fig_num=0;
ymax=[5 10];ymin=[-2,-5];
for event_idx2=1:event_idx1
pred_rms_mat=zeros(thr_idx1,1);
for thr_idx2=1:thr_idx1
fig_num=fig_num+1;
H_pred_erp=figure(fig_num);
set(gcf,'PaperPositionMode', 'manual','Position',get(0, 'Screensize'),'PaperOrientation', 'landscape');
pred_rms_mat(thr_idx2,1)=dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).rms_erp_pred;
pred_time= dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).time_pred;
pred_erp= dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).erp_pred;
plot(pred_time,pred_erp, 'LineWidth',3);
hold on
plot(pred_time,dynamics_windowed_inc.(event_name{event_idx2}).eegdata_rec, 'LineWidth',3);
%%%%Axes
axis_font=30;
ax=gca;
ax.YLabel.String = 'Potential(\muV)';ax.XLabel.String = 'Time(sec)';
ax.FontSize = axis_font;ax.FontWeight = 'bold';
ax.YLabel.FontSize=axis_font; ax.XLabel.FontSize=axis_font;
ax.YLabel.FontWeight='b'; ax.XLabel.FontWeight='b';
ax.XLim=[pred_time(1),pred_time(end)];
ax.YLim=[ymin(event_idx2),ymax(event_idx2)];
grid on
%%%%Title
ax.Title.String = strcat('Incremental Windowed DMD (\sigma_{thr} =', num2str(thresh_vec(thr_idx2)),')');
ax.Title.FontWeight = 'bold';ax.Title.FontSize = axis_font;
%%%%%%%
rms_thr_fig=strcat(ERP_Pred_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_pred_',thresh_str_vec{thr_idx2},'.fig');
rms_thr_pdf=strcat(ERP_Pred_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_pred_',thresh_str_vec{thr_idx2});
saveas(H_pred_erp,rms_thr_fig);
print(rms_thr_pdf,'-dpdf','-fillpage')
end
axis_font=30;lgd_font=30;
fig_num=fig_num+1;
H_pred_rms_bar=figure(fig_num);
set(gcf,'PaperPositionMode', 'manual','Position',get(0, 'Screensize'),'PaperOrientation', 'landscape');
bar(pred_rms_mat)
%%%%Axes
ax=gca;
ax.YLabel.String = 'Normalized RMS Error';ax.XLabel.String ='\sigma_{thr}';
ax.FontSize = axis_font;ax.FontWeight = 'b';
ax.YLabel.FontSize=axis_font; ax.XLabel.FontSize=axis_font;
ax.YLabel.FontWeight='b'; ax.XLabel.FontWeight='b';
ax.XTickLabel=threshold_label;
ax.YLim=[0,max(max(pred_rms_mat))+0.2];
grid on
%%%%Title
ax.Title.String = sprintf('%s Event',event_name{event_idx2});
ax.Title.FontWeight = 'bold';ax.Title.FontSize = axis_font;
%%%% Saving Image
erprms_thr_fig=strcat(ERP_Pred_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_pred_rms.fig');
erprms_thr_pdf=strcat(ERP_Pred_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_pred_rms');
saveas(H_pred_rms_bar,erprms_thr_fig);
print(erprms_thr_pdf,'-dpdf','-fillpage')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Plotting Reconstructed ERP
close all
ymax=[3 10];ymin=[-2,-4];
for event_idx2=1:event_idx1
recon_rms_mat=zeros(thr_idx1,1);
for thr_idx2=1:thr_idx1
fig_num=fig_num+1;
H_recon_erp=figure(fig_num);
set(gcf,'PaperPositionMode', 'manual','Position',get(0, 'Screensize'),'PaperOrientation', 'landscape');
recon_rms_mat(thr_idx2,1)=dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).rms_erp_recon;
recon_time= dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).time_recon;
recon_eeg= dynamics_windowed_inc.(event_name{event_idx2}).(thresh_str_vec{thr_idx2}).erp_recon;
plot(recon_time,recon_eeg, 'LineWidth',3);
plot(recon_time,dynamics_windowed_inc.(event_name{event_idx2}).eegdata_rec, 'LineWidth',3);
%%%%Axes
axis_font=30;
ax=gca;
ax.YLabel.String = 'Potential(\muV)';ax.XLabel.String = 'Time(sec)';
ax.FontSize = axis_font;ax.FontWeight = 'bold';
ax.YLabel.FontSize=axis_font; ax.XLabel.FontSize=axis_font;
ax.YLabel.FontWeight='b'; ax.XLabel.FontWeight='b';
ax.XLim=[recon_time(1),recon_time(end)];
ax.YLim=[ymin(event_idx2),ymax(event_idx2)];
grid on
%%%%Title
ax.Title.String = strcat('Incremental Windwed DMD (\sigma_{thr} =', num2str(thresh_vec(thr_idx2)),')');
ax.Title.FontWeight = 'bold';ax.Title.FontSize = axis_font;
%%%%%%%
rms_thr_fig=strcat(ERP_Recon_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_recon_',thresh_str_vec{thr_idx2},'.fig');
rms_thr_png=strcat(ERP_Recon_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_recon_',thresh_str_vec{thr_idx2});
saveas(H_recon_erp,rms_thr_fig);
print(rms_thr_png,'-dpdf','-fillpage')
end
axis_font=30;
fig_num=fig_num+1;
H_recon_rms_bar=figure(fig_num);
set(gcf,'PaperPositionMode', 'manual','Position',get(0, 'Screensize'),'PaperOrientation', 'landscape');
bar(recon_rms_mat)
%%%%Axes
ax=gca;
ax.YLabel.String = 'Normalized RMS Error';ax.XLabel.String ='\sigma_{thr}';
ax.FontSize = axis_font;ax.FontWeight = 'b';
ax.YLabel.FontSize=axis_font; ax.XLabel.FontSize=axis_font;
ax.YLabel.FontWeight='b'; ax.XLabel.FontWeight='b';
ax.XTickLabel=threshold_label;
ax.YLim=[0,max(max(recon_rms_mat))+0.1];
grid on
%%%%Title
ax.Title.String = sprintf('%s Event',event_name{event_idx2});
ax.Title.FontWeight = 'bold';ax.Title.FontSize = axis_font;
%%%% Saving Image
erprms_thr_fig=strcat(ERP_Recon_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_recon_rms.fig');
erprms_thr_png=strcat(ERP_Recon_figures,'\',event_name{event_idx2},'_inc_windowed_DMD_recon_rms');
saveas(H_recon_rms_bar,erprms_thr_fig);
print(erprms_thr_png,'-dpdf','-fillpage')
end