%% 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.
                
% These are the constants defining the matrix Y1               
NumPhotos=109;   %There are 109 frames, or photos, in this data set.
pm=120;
pn=160;          % Each photo is pm x pn (in this case, 120 x 160).
                
% We can visualize the "movie"
figure(1)
for j=1:NumPhotos
   A=reshape(Y1(:,j),pm,pn);
   imagesc(A); colormap(gray); axis equal; axis off;
   pause(0.1)
end

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

%% Mean subtraction
Ymean=mean(Y1,2);
figure(2)
imagesc(reshape(Ymean,pm,pn)); colormap(gray); axis equal; axis off;
title('The Mean');

%% The SVD
% We'll mean subtract, but keep the original data intact.  We'll call put
% the mean subtracted data in matrix X.
X=Y1-repmat(Ymean,1,NumPhotos);
[U,S,V]=svd(X,'econ');

%% Visualize the basis vectors- Here are 4 of them
figure(3)
for j=1:4
    subplot(2,2,j)
    imagesc(reshape(U(:,j),pm,pn)); colormap(gray); axis equal; axis off
end
title('The first four basis vectors');

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

figure(4)
plot(Xcoords(1,:),Xcoords(2,:),'.');
title('Best two dimensional basis');

%% The Best five dimensional reconstruction as a "movie"
% Uncomment and run if you want to see the movie
%figure(5)
%Xcoords=U(:,1:5)'*X;
%Recon=U(:,1:5)*Xcoords;  %Note:  This is UU^Tx, or the projection.
% for j=1:NumPhotos
%    A=reshape(Recon(:,j)+Ymean,pm,pn);
%    imagesc(A); colormap(gray); axis equal; axis off;
%    pause(0.1);  %Make this longer or shorter to see each frame.
% end