PCA - Principle Components Analyses

close all;
clear all;
clc;
 
% VARIABLES
vars = 2;
samples = 20;
nComponents = 2;
 
% 1) Normalize data
    data=rand(vars,samples);
% 2) Remove mean
    MeanMatrix = repmat(mean(data,2),1,size(data,2));
    data=data-MeanMatrix;
% 3) Calculate covariance matrix
    CovMatrix = cov(data');
% 3) Calculate eigenvectors and eigenvalues of the covariance matrix
    [FeatureMatrix, EvalueMatrix] = eig(CovMatrix);
    Evalues = diag(EvalueMatrix)
% 4) Order by eigenvalue
    Evalues = Evalues(end:-1:1)
    FeatureMatrix = FeatureMatrix(:,end:-1:1);
    FeatureMatrix=FeatureMatrix';  
% 5) Take first n E-vectors
    FeatureMatrix = FeatureMatrix(1:nComponents,:);
% 6) Project data
    ProjectedData = FeatureMatrix * data;
% 7) Reconstruction
    ReconstructedData = (FeatureMatrix' * ProjectedData) + MeanMatrix;
 
% plot
subplot(2,2,1);
plot(data(1,:),data(2,:),'.');   
subplot(2,2,2);
plot(ProjectedData(1,:),ProjectedData(2,:),'.');  
subplot(2,2,3);
plot(ReconstructedData(1,:),ReconstructedData(2,:),'.');