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data_analysis.m
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data_analysis.m
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clc
close all
clear all
%% LOAD TRAINING DATA
data_P300_path = 'Donnees8/ref_P300';
data_NP300_path = 'Donnees8/ref_NP300';
load(data_P300_path);
load(data_NP300_path);
%% DATA ANALYSIS
%% Histograms - P300
figure(1)
nbins = 30;
histogram(ref_P300(:,1),nbins)
hold on
histogram(ref_P300(:,2),nbins)
hold on
histogram(ref_P300(:,3),nbins)
hold on
histogram(ref_P300(:,4),nbins)
legend('E1','E2','E3','E4')
title('P300 Histogram')
hold off
%% Histograms - NP300
figure(3)
nbins = 30;
histogram(ref_NP300(:,1),nbins)
hold on
histogram(ref_NP300(:,2),nbins)
hold on
histogram(ref_NP300(:,3),nbins)
hold on
histogram(ref_NP300(:,4),nbins)
legend('E1','E2','E3','E4')
title('NP300 Histogram')
hold off
%% Plot Distribution 4D - P300
figure(15)
scatter3(ref_P300(:,1),ref_P300(:,2),ref_P300(:,3),30,ref_P300(:,4),'filled')
xlabel('E1')
ylabel('E2')
zlabel('E3')
cb = colorbar;
cb.Label.String = 'E4';
title('P300 Distribution')
%% Plot Distribution 4D - NP300
figure(16)
scatter3(ref_NP300(:,1),ref_NP300(:,2),ref_NP300(:,3),30,ref_NP300(:,4),'filled')
xlabel('E1')
ylabel('E2')
zlabel('E3')
cb = colorbar;
cb.Label.String = 'E4';
title('NP300 Distribution')
%% Plot Distribution 4D - P300 And NP300
% E4 Colored
figure(17)
hold on
hP300 = scatter3(ref_P300(:,1),ref_P300(:,2),ref_P300(:,3),30,ref_P300(:,4),'filled','o','MarkerEdgeColor',[1 0 0],'LineWidth',2);
hNP300 = scatter3(ref_NP300(:,1),ref_NP300(:,2),ref_NP300(:,3),50,ref_NP300(:,4),'filled','s','MarkerEdgeColor',[0 0 0]);
xlabel('E1')
ylabel('E2')
zlabel('E3')
cb = colorbar;
cb.Label.String = 'E4';
title('P300 And NP300 Distribution')
legend('P300','NP300')
grid('on')
hold off
% E3 Colored
figure(18)
hold on
hP300 = scatter3(ref_P300(:,4),ref_P300(:,1),ref_P300(:,2),30,ref_P300(:,3),'filled','o','MarkerEdgeColor',[1 0 0],'LineWidth',2);
hNP300 = scatter3(ref_NP300(:,4),ref_NP300(:,1),ref_NP300(:,2),50,ref_NP300(:,3),'filled','s','MarkerEdgeColor',[0 0 0]);
xlabel('E4')
ylabel('E1')
zlabel('E2')
cb = colorbar;
cb.Label.String = 'E3';
title('P300 And NP300 Distribution')
legend('P300','NP300')
grid('on')
hold off
% E2 Colored
figure(19)
hold on
hP300 = scatter3(ref_P300(:,3),ref_P300(:,4),ref_P300(:,1),30,ref_P300(:,2),'filled','o','MarkerEdgeColor',[1 0 0],'LineWidth',2);
hNP300 = scatter3(ref_NP300(:,3),ref_NP300(:,4),ref_NP300(:,1),50,ref_NP300(:,2),'filled','s','MarkerEdgeColor',[0 0 0]);
xlabel('E3')
ylabel('E4')
zlabel('E1')
cb = colorbar;
cb.Label.String = 'E2';
title('P300 And NP300 Distribution')
legend('P300','NP300')
grid('on')
hold off
% E1 Colored
figure(20)
hold on
hP300 = scatter3(ref_P300(:,2),ref_P300(:,3),ref_P300(:,4),30,ref_P300(:,1),'filled','o','MarkerEdgeColor',[1 0 0],'LineWidth',2);
hNP300 = scatter3(ref_NP300(:,2),ref_NP300(:,3),ref_NP300(:,4),50,ref_NP300(:,1),'filled','s','MarkerEdgeColor',[0 0 0]);
xlabel('E2')
ylabel('E3')
zlabel('E4')
cb = colorbar;
cb.Label.String = 'E1';
title('P300 And NP300 Distribution')
legend('P300','NP300')
grid('on')
hold off
%% Histograms - P300 And NP300
% E1
figure(21)
nbins = 30;
histogram(ref_P300(:,1),nbins)
hold on
histogram(ref_NP300(:,1),nbins)
legend('P300','NP300')
title('E1 Parameter Histogram')
hold off
% E2
figure(22)
nbins = 30;
histogram(ref_P300(:,2),nbins)
hold on
histogram(ref_NP300(:,2),nbins)
legend('P300','NP300')
title('E2 Parameter Histogram')
hold off
% E3
figure(23)
nbins = 30;
histogram(ref_P300(:,3),nbins)
hold on
histogram(ref_NP300(:,3),nbins)
legend('P300','NP300')
title('E3 Parameter Histogram')
hold off
% E4
figure(24)
nbins = 30;
histogram(ref_P300(:,4),nbins)
hold on
histogram(ref_NP300(:,4),nbins)
legend('P300','NP300')
title('E4 Parameter Histogram')
hold off
%% Mean - P300
mean_E1_P300 = sum(ref_P300(:,1))/length(ref_P300(:,1));
mean_E2_P300 = sum(ref_P300(:,2))/length(ref_P300(:,2));
mean_E3_P300 = sum(ref_P300(:,3))/length(ref_P300(:,3));
mean_E4_P300 = sum(ref_P300(:,4))/length(ref_P300(:,4));
mP300 = [mean_E1_P300; mean_E2_P300; mean_E3_P300; mean_E4_P300];
%% Mean - NP300
mean_E1_NP300 = sum(ref_NP300(:,1))/length(ref_NP300(:,1));
mean_E2_NP300 = sum(ref_NP300(:,2))/length(ref_NP300(:,2));
mean_E3_NP300 = sum(ref_NP300(:,3))/length(ref_NP300(:,3));
mean_E4_NP300 = sum(ref_NP300(:,4))/length(ref_NP300(:,4));
mNP300 = [mean_E1_NP300; mean_E2_NP300; mean_E3_NP300; mean_E4_NP300];
%% Covariance - P300
ctmpE11 = [(ref_P300(:,1)-mP300(1)) (ref_P300(:,1)-mP300(1))];
ctmpE12 = [(ref_P300(:,1)-mP300(1)) (ref_P300(:,2)-mP300(2))];
ctmpE13 = [(ref_P300(:,1)-mP300(1)) (ref_P300(:,3)-mP300(3))];
ctmpE14 = [(ref_P300(:,1)-mP300(1)) (ref_P300(:,4)-mP300(4))];
ctmpE21 = [(ref_P300(:,2)-mP300(2)) (ref_P300(:,1)-mP300(1))];
ctmpE22 = [(ref_P300(:,2)-mP300(2)) (ref_P300(:,2)-mP300(2))];
ctmpE23 = [(ref_P300(:,2)-mP300(2)) (ref_P300(:,3)-mP300(3))];
ctmpE24 = [(ref_P300(:,2)-mP300(2)) (ref_P300(:,4)-mP300(4))];
ctmpE31 = [(ref_P300(:,3)-mP300(3)) (ref_P300(:,1)-mP300(1))];
ctmpE32 = [(ref_P300(:,3)-mP300(3)) (ref_P300(:,2)-mP300(2))];
ctmpE33 = [(ref_P300(:,3)-mP300(3)) (ref_P300(:,3)-mP300(3))];
ctmpE34 = [(ref_P300(:,3)-mP300(3)) (ref_P300(:,4)-mP300(4))];
ctmpE41 = [(ref_P300(:,4)-mP300(4)) (ref_P300(:,1)-mP300(1))];
ctmpE42 = [(ref_P300(:,4)-mP300(4)) (ref_P300(:,2)-mP300(2))];
ctmpE43 = [(ref_P300(:,4)-mP300(4)) (ref_P300(:,3)-mP300(3))];
ctmpE44 = [(ref_P300(:,4)-mP300(4)) (ref_P300(:,4)-mP300(4))];
CoE11 = (ctmpE11(:,1)' * ctmpE11(:,2)) / (length(ctmpE11)-1);
CoE12 = (ctmpE12(:,1)' * ctmpE12(:,2)) / (length(ctmpE12)-1);
CoE13 = (ctmpE13(:,1)' * ctmpE13(:,2)) / (length(ctmpE13)-1);
CoE14 = (ctmpE14(:,1)' * ctmpE14(:,2)) / (length(ctmpE14)-1);
CoE21 = (ctmpE21(:,1)' * ctmpE21(:,2)) / (length(ctmpE21)-1);
CoE22 = (ctmpE22(:,1)' * ctmpE22(:,2)) / (length(ctmpE22)-1);
CoE23 = (ctmpE23(:,1)' * ctmpE23(:,2)) / (length(ctmpE23)-1);
CoE24 = (ctmpE24(:,1)' * ctmpE24(:,2)) / (length(ctmpE24)-1);
CoE31 = (ctmpE31(:,1)' * ctmpE31(:,2)) / (length(ctmpE31)-1);
CoE32 = (ctmpE32(:,1)' * ctmpE32(:,2)) / (length(ctmpE32)-1);
CoE33 = (ctmpE33(:,1)' * ctmpE33(:,2)) / (length(ctmpE33)-1);
CoE34 = (ctmpE34(:,1)' * ctmpE34(:,2)) / (length(ctmpE34)-1);
CoE41 = (ctmpE41(:,1)' * ctmpE41(:,2)) / (length(ctmpE41)-1);
CoE42 = (ctmpE42(:,1)' * ctmpE42(:,2)) / (length(ctmpE42)-1);
CoE43 = (ctmpE43(:,1)' * ctmpE43(:,2)) / (length(ctmpE43)-1);
CoE44 = (ctmpE44(:,1)' * ctmpE44(:,2)) / (length(ctmpE44)-1);
CoP300 = [CoE11 CoE12 CoE13 CoE14 ; CoE21 CoE22 CoE23 CoE24; CoE31 CoE32 CoE33 CoE34; CoE41 CoE42 CoE43 CoE44];
%% Covariance - NP300
ctmpE11 = [(ref_NP300(:,1)-mNP300(1)) (ref_NP300(:,1)-mNP300(1))];
ctmpE12 = [(ref_NP300(:,1)-mNP300(1)) (ref_NP300(:,2)-mNP300(2))];
ctmpE13 = [(ref_NP300(:,1)-mNP300(1)) (ref_NP300(:,3)-mNP300(3))];
ctmpE14 = [(ref_NP300(:,1)-mNP300(1)) (ref_NP300(:,4)-mNP300(4))];
ctmpE21 = [(ref_NP300(:,2)-mNP300(2)) (ref_NP300(:,1)-mNP300(1))];
ctmpE22 = [(ref_NP300(:,2)-mNP300(2)) (ref_NP300(:,2)-mNP300(2))];
ctmpE23 = [(ref_NP300(:,2)-mNP300(2)) (ref_NP300(:,3)-mNP300(3))];
ctmpE24 = [(ref_NP300(:,2)-mNP300(2)) (ref_NP300(:,4)-mNP300(4))];
ctmpE31 = [(ref_NP300(:,3)-mNP300(3)) (ref_NP300(:,1)-mNP300(1))];
ctmpE32 = [(ref_NP300(:,3)-mNP300(3)) (ref_NP300(:,2)-mNP300(2))];
ctmpE33 = [(ref_NP300(:,3)-mNP300(3)) (ref_NP300(:,3)-mNP300(3))];
ctmpE34 = [(ref_NP300(:,3)-mNP300(3)) (ref_NP300(:,4)-mNP300(4))];
ctmpE41 = [(ref_NP300(:,4)-mNP300(4)) (ref_NP300(:,1)-mNP300(1))];
ctmpE42 = [(ref_NP300(:,4)-mNP300(4)) (ref_NP300(:,2)-mNP300(2))];
ctmpE43 = [(ref_NP300(:,4)-mNP300(4)) (ref_NP300(:,3)-mNP300(3))];
ctmpE44 = [(ref_NP300(:,4)-mNP300(4)) (ref_NP300(:,4)-mNP300(4))];
CoE11 = (ctmpE11(:,1)' * ctmpE11(:,2)) / (length(ctmpE11)-1);
CoE12 = (ctmpE12(:,1)' * ctmpE12(:,2)) / (length(ctmpE12)-1);
CoE13 = (ctmpE13(:,1)' * ctmpE13(:,2)) / (length(ctmpE13)-1);
CoE14 = (ctmpE14(:,1)' * ctmpE14(:,2)) / (length(ctmpE14)-1);
CoE21 = (ctmpE21(:,1)' * ctmpE21(:,2)) / (length(ctmpE21)-1);
CoE22 = (ctmpE22(:,1)' * ctmpE22(:,2)) / (length(ctmpE22)-1);
CoE23 = (ctmpE23(:,1)' * ctmpE23(:,2)) / (length(ctmpE23)-1);
CoE24 = (ctmpE24(:,1)' * ctmpE24(:,2)) / (length(ctmpE24)-1);
CoE31 = (ctmpE31(:,1)' * ctmpE31(:,2)) / (length(ctmpE31)-1);
CoE32 = (ctmpE32(:,1)' * ctmpE32(:,2)) / (length(ctmpE32)-1);
CoE33 = (ctmpE33(:,1)' * ctmpE33(:,2)) / (length(ctmpE33)-1);
CoE34 = (ctmpE34(:,1)' * ctmpE34(:,2)) / (length(ctmpE34)-1);
CoE41 = (ctmpE41(:,1)' * ctmpE41(:,2)) / (length(ctmpE41)-1);
CoE42 = (ctmpE42(:,1)' * ctmpE42(:,2)) / (length(ctmpE42)-1);
CoE43 = (ctmpE43(:,1)' * ctmpE43(:,2)) / (length(ctmpE43)-1);
CoE44 = (ctmpE44(:,1)' * ctmpE44(:,2)) / (length(ctmpE44)-1);
CoNP300 = [CoE11 CoE12 CoE13 CoE14 ; CoE21 CoE22 CoE23 CoE24; CoE31 CoE32 CoE33 CoE34; CoE41 CoE42 CoE43 CoE44];
% PCA
coeffPCA_ref_P300 = pca(ref_P300,'Algorithm','eig','Rows','all');
coeffPCA_ref_NP300 = pca(ref_NP300,'Algorithm','eig','Rows','all');
%% Eigenvalues And Eigenvectors
%P300
syms lenda
eqn1 = det(CoP300 - lenda * eye(size(CoP300))) == 0;
eigen_values = vpasolve(eqn1,lenda);
[eigen_vectors_CoP300,diag_eigen_values_CoP300] = eig(CoP300);
%NP300
syms lenda
eqn2 = det(CoNP300 - lenda * eye(size(CoNP300))) == 0;
eigen_values = vpasolve(eqn2,lenda);
[eigen_vectors_CoNP300,diag_eigen_values_CoNP300] = eig(CoNP300);
%% Note : Projection proj(u)->v =(u*v/(||v||^2))*v
%% Density probability P300 and NP300
[nRowP300, nColP300] = size(ref_P300);
[nRowNP300, nColNP300] = size(ref_NP300);
clear pd_P300
for i = 1:nColP300
pd_P300(i) = fitdist(ref_P300(:,i),'normal');
end
clear pd_NP300
for i = 1:nColNP300
pd_NP300(i) = fitdist(ref_NP300(:,i),'normal');
end