UFLDL教程之三：PCA & Whitening

参考：

具体可参考： http://www.cnblogs.com/tornadomeet/archive/2013/03/21/2973631.html
close all

%%================================================================

%% Step 0: Load data

% We have provided the code to load data from pcaData.txt into x.

% x is a 2 * 45 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(1);

scatter(x(1, :), x(2, :));

title('Raw data');

%%================================================================

%% Step 1a: 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, 1)); % You need to compute this

%avg = mean(x, 1); %

%x = x - repmat(avg, size(x, 1), 1);

sigma = x * x' / size(x, 2);

[u s v] = svd(sigma);

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

hold on

plot([0 u(1,1)], [0 u(2,1)]);

plot([0 u(1,2)], [0 u(2,2)]);

scatter(x(1, :), x(2, :));

hold off

%%================================================================

%% Step 1b: 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(2);

scatter(xRot(1, :), xRot(2, :));

title('xRot');

%%================================================================

%% Step 2: Reduce the number of dimensions from 2 to 1.

% Compute xRot again (this time projecting to 1 dimension).

% Then, compute xHat by projecting the xRot back onto the original axes

% to see the effect of dimension reduction

% -------------------- YOUR CODE HERE --------------------

k = 1; % Use k = 1 and project the data onto the first eigenbasis

xHat = zeros(size(x)); % You need to compute this

xHat = u*([u(:,1:k), zeros(size(x,1),1)]' * x); %

%xHat = u*([u(:,1),zeros(n,1)]'*x);

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

figure(3);

scatter(xHat(1, :), xHat(2, :));

title('xHat');

%%================================================================

%% Step 3: PCA Whitening

% Complute xPCAWhite and plot the results.

epsilon = 1e-5;

% -------------------- YOUR CODE HERE --------------------

xPCAWhite = zeros(size(x)); % You need to compute this

xPCAWhite = diag(1./sqrt(diag(s) + epsilon)) * u' * x;

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

figure(4);

scatter(xPCAWhite(1, :), xPCAWhite(2, :));

title('xPCAWhite');

%%================================================================

%% Step 3: ZCA Whitening

% Complute xZCAWhite and plot the results.

% -------------------- YOUR CODE HERE --------------------

xZCAWhite = zeros(size(x)); % You need to compute this

xZCAWhite = u * diag(1./sqrt(diag(s) + epsilon)) * u' * x;

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

figure(5);

scatter(xZCAWhite(1, :), xZCAWhite(2, :));

title('xZCAWhite');

%% Congratulations! When you have reached this point, you are done!

% You can now move onto the next PCA exercise. :)