%% 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 author
Y1=double(Y1);  %Changes the data from "integers" to "floating point"
                %The data was saved as integers to save on memory.

% We can visualize the "movie"
figure(1)
for j=1:109
   A=reshape(Y1(:,j),120,160);
   imagesc(A); colormap(gray); axis equal; axis off;
   pause(0.1)
end

% Now that we've all had a good laugh, let's continue.

%% Find the mean of the collection, subtract it (different label to save the original data)
Ymean=mean(Y1,2);
figure(2)
imagesc(reshape(Ymean,120,160)); colormap(gray); axis equal; axis off;
title('The Movie Mean');

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(tempS);
title('The Eigenvalues of X^TX (Singular Values squared)')

%% Visualize the basis vectors- Here are 4 of them
figure(4)
for j=1:4
    subplot(2,2,j)
    imagesc(reshape(U(:,j),120,160)); colormap(gray); axis equal; axis off
end
title('The first four basis vectors');

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

figure(5)
plot(Coord(1,:),Coord(2,:),'.');
title('The movie data presented in the best two dimensional basis');

%% The Best two dimensional reconstruction as a movie

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

figure(6)
 for j=1:109
    A=reshape(Recon(:,j),120,160);
    imagesc(A); colormap(gray); axis equal; axis off;
    M(j)=getframe;
    pause(0.05)
 end