UFLDL Exercise:PCA in 2D

1. result

2. code

close all

%%================================================================
%% Step : Load data
%  We have provided the code to load data from pcaData.txt into x.
%  x is a  *  matrix, where the kth column x(:,k) corresponds to
%  the kth data point.Here we provide the code to load natural image data into x.
%  You do not need to change the code below.

x = load('pcaData.txt','-ascii');
figure();
scatter(x(, :), x(, :));
title('Raw data');


%%================================================================
%% Step a: Implement PCA to obtain U 
%  Implement PCA to obtain the rotation matrix U, which is the eigenbasis
%  sigma. 

% -------------------- YOUR CODE HERE -------------------- 
u = zeros(size(x, )); % You need to compute this
%x = bsxfun(@minus, x, mean(x, ));
sigma = x * x' / size(x, );
[u,s,v] = svd(sigma);
% -------------------------------------------------------- 
hold on
plot([ u(,)], [ u(,)]);
plot([ u(,)], [ u(,)]);
scatter(x(, :), x(, :));
hold off

%%================================================================
%% Step b: Compute xRot, the projection on to the eigenbasis
%  Now, compute xRot by projecting the data on to the basis defined
%  by U. Visualize the points by performing a scatter plot.

% -------------------- YOUR CODE HERE -------------------- 
xRot = zeros(size(x)); % You need to compute this
xRot = u' * x;

% -------------------------------------------------------- 

% Visualise the covariance matrix. You should see a line across the
% diagonal against a blue background.
figure();
scatter(xRot(, :), xRot(, :));
title('xRot');

%%================================================================
%% Step : Reduce the number of dimensions from  to  
%  Compute xRot again (this time projecting to  dimension).
%  Then, compute xHat by projecting the xRot back onto the original axes 
%  to see the effect of dimension reduction

% -------------------- YOUR CODE HERE -------------------- 
k = ; % Use k =  and project the data onto the first eigenbasis
xHat = zeros(size(x)); % You need to compute this
tx = xRot;
tx(k+:size(xRot,),:) = zeros(size(xRot,)-k,size(xRot,));
xHat = u * tx;

% -------------------------------------------------------- 
figure();
scatter(xHat(, :), xHat(, :));
title('xHat');


%%================================================================
%% Step : PCA Whitening
%  Complute xPCAWhite and plot the results.

epsilon = ;
% -------------------- YOUR CODE HERE -------------------- 
xPCAWhite = zeros(size(x)); % You need to compute this
xPCAWhite = diag(/sqrt(diag(s)+epsilon)) * xRot;



% -------------------------------------------------------- 
figure();
scatter(xPCAWhite(, :), xPCAWhite(, :));
title('xPCAWhite');

%%================================================================
%% Step : ZCA Whitening
%  Complute xZCAWhite and plot the results.

% -------------------- YOUR CODE HERE -------------------- 
xZCAWhite = zeros(size(x)); % You need to compute this
xZCAWhite = u * xPCAWhite;

% -------------------------------------------------------- 
figure();
scatter(xZCAWhite(, :), xZCAWhite(, :));
title('xZCAWhite');

%% Congratulations! When you have reached this point, you are done!
%  You can now move onto the next PCA exercise. :)