Exercise:PCA and Whitening 代码示例

Exercise:PCA and Whitening 代码示例

练习参考PCA and Whitening，与上一个练习基本一致。

 

更改图像数据的均值

 

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

 

Implement PCA to obtain xRot

 

xRot = zeros(size(x));
sigma = x * x' / size(x,2);
[u,s,v] = svd(sigma);
xRot = u' * x;

 

Check your implementation of PCA

 

covar = zeros(size(x, 1));
covar = xRot * xRot' / size(xRot,2);

 

Find k, the number of components to retain

 

k = 0; % Set k accordingly
all = sum(diag(s));
for i=1:size(s,1)
    if sum(diag(s(1:i,1:i))) / all >= 0.99
        k = i;
        break;
    end
end

 

 

Implement PCA with dimension reduction

 

xHat = zeros(size(x));
xTilde = u(:,1:k)' * x;
xHat = u(:,1:k) * xTilde;

 

 

Implement PCA with whitening and regularisation

 

epsilon = 0.1;
xPCAWhite = zeros(size(x));
xPCAWhite = diag(sqrt(1./(diag(s) + epsilon))) * xRot;

 

 

Check your implementation of PCA whitening 

 

covar = xPCAWhite * xPCAWhite' / size(xPCAWhite,2)

 

 

Implement ZCA whitening

 

xZCAWhite = zeros(size(x));
xZCAWhite = u * xPCAWhite;