pca.m

% PCA 
% Written by SIAMAK FARIDANI
% I used this tutotial
% www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf

clc;
close all;
clear all;

numdata=20; %should be even

%step 1, generating a dataset
x1=rand(numdata/2,1);
y1=rand(numdata/2,1);
x2=3*rand(numdata/2,1)+3;
y2=3*rand(numdata/2,1)+3;

x=[x1;x2];
y=[y1;y2];

%step 2, finding a mean and subtracting
xmean=mean(x);
ymean=mean(y);

xnew=x-xmean*ones(numdata,1);
ynew=y-ymean*ones(numdata,1);

subplot(3,1,1);
plot(x,y, 'o');
title('Original Data');

%Uncomment to see the data after the deduction of the mean
%subplot(4,1,2);
%plot(xnew,ynew, 'o');
%title('mean is deducted')

%step 3, covariance matrix
covariancematrix=cov(xnew,ynew);

%step 4, Finding Eigenvectors
[V,D] = eig(covariancematrix);
D=diag(D);
maxeigval=V(:,find(D==max(D)));


%step 5, Deriving the new data set
%finding the projection onto the eigenvectors

finaldata=maxeigval'*[xnew,ynew]';
subplot(3,1,2);
stem(finaldata, 'DisplayName', 'finaldata', 'YDataSource', 'finaldata');
title('PCA 1D output ')
%we do a classification now
subplot(3,1,3);
title('Final Classification')
hold on
for i=1:size(finaldata,2)
    if  finaldata(i)>=0
        plot(x(i),y(i),'o')
        plot(x(i),y(i),'r*')
        
    else
        plot(x(i),y(i),'o')
        plot(x(i),y(i),'g*')
    end
    
end