%% Sample script for the "author" data

% Some cleaning commands:
close all;  %Close all open figures
clear       %Clear the memory
clc         %Clear the command window

% Download the data from the class website, so it can be loaded here:
load FacesNoRem
Y1=double(Y);  %Changes the data from "integers" to "floating point"
                %The data was saved as integers to save on memory.

% We can visualize the first 4 faces:
figure(1)
for j=1:4
   temp=reshape(Y1(:,j),294,262);
   imagesc(temp); 
   colormap(gray); axis equal; axis off;
end

%% Find the mean of the collection, subtract it (different label to save the original data)
Ymean=mean(Y1,2);
figure(2)
% Plot the mean face:


X=Y1-repmat(Ymean,1,109);

%% The SVD

[U,S,V]=svd(X,'econ');
tempS=diag(S).^2;
tempS=tempS/sum(tempS);   %Normalized eigenvalues.

figure(3)

% Plot the normalized eigenvalues


%% Visualize the basis vectors- Here are 4 of them
figure(4)

% Plot the first four eigenvectors as images


%% Projection to R^2
Coord=U(:,1:2)'*X;   %The matrix Xcoords is now 2 x 109

figure(5)

% Plot the two dimensional coordinates:



%% Visualize the reconstructed faces:

Recon=U(:,1:2)*Coord;

% Plot some of the reconstructed faces: