主成分分析与白化，这部分很简单，当然，其实是用Matlab比较简单，要是自己写SVD分解算法，足够研究好几个月的了。下面是我自己实现的练习答案，不保证完全正确，不过结果和网站上面给出的基本一致。

1.PCA in 2D

1.1 Step 1a: Implement PCA to obtain U

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

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

[u,s,v]=svd(sigma);

1.2 Step 1b: Compute xRot, the projection on to the eigenbasis

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

xRot=u'*x;

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

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

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

x_ap=u(:,:k)'*x;

xHat(:k,:)=x_ap;

xHat=u*xHat;

1.4 Step 3: PCA Whitening

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

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

1.5 Step 3: ZCA Whitening

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

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

2.PCA and Whitening

2.1 Step 0b: Zero-mean the data (by row)

avg = mean(x, );

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

2.2 Step 1a: Implement PCA to obtain xRot

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

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

[U,S,V]=svd(sigma);

xRot=U'*x;

2.3 Step 1b: Check your implementation of PCA

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

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

2.4 Step 2: Find k, the number of components to retain

k = ; % Set k accordingly

sum_k=;

sum=trace(S);

for k=:size(S,)

    sum_k=sum_k+S(k,k);

    if(sum_k/sum>=0.99) %0.9

        break;

    end

end

2.5 Step 3: Implement PCA with dimension reduction

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

xTilde = U(:,:k)' * x;

xHat(:k,:)=xTilde;

xHat=U*xHat;

2.6 Step 4a: Implement PCA with whitening and regularisation

xPCAWhite = diag(./sqrt(diag(S) + epsilon)) * U' * x;

2.7 Step 4b: Check your implementation of PCA whitening

covar = zeros(size(xPCAWhite, ));

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

2.8 Step 5: Implement ZCA whitening

xZCAWhite=U * diag(./sqrt(diag(S) + epsilon)) * U' * x;

巴特西

UFLDL教程练习（exercise）答案（2）

主成分分析与白化，这部分很简单，当然，其实是用Matlab比较简单，要是自己写SVD分解算法，足够研究好几个月的了。下面是我自己实现的练习答案，不保证完全正确，不过结果和网站上面给出的基本一致。

1.PCA in 2D

2.PCA and Whitening

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