自然圖片的PCA白化

在這個練習里面我們將實現PCA和ZCA白化。首先先下載這個文件pca_exercise.zip,?然后我們解壓它，并用matlab打開它，我們只需要更改pca_gen.m.這個文件。

然后把代碼改成下面這個形式

%%================================================================ %% Step 0a: Load data % Here we provide the code to load natural image data into x. % x will be a 144 * 10000 matrix, where the kth column x(:, k) corresponds to % the raw image data from the kth 12x12 image patch sampled. % You do not need to change the code below.x = sampleIMAGESRAW(); figure('name','Raw images'); randsel = randi(size(x,2),200,1); % A random selection of samples for visualization display_network(x(:,randsel));%%================================================================ %% Step 0b: Zero-mean the data (by row) % You can make use of the mean and repmat/bsxfun functions.% -------------------- YOUR CODE HERE -------------------- x=x-repmat(mean(x),size(x,1),1); %%================================================================ %% Step 1a: Implement PCA to obtain xRot % Implement PCA to obtain xRot, the matrix in which the data is expressed % with respect to the eigenbasis of sigma, which is the matrix U.% -------------------- YOUR CODE HERE -------------------- xRot = zeros(size(x)); % You need to compute this [u,s,v]=svd(x); xRot=u'*x;%%================================================================ %% Step 1b: Check your implementation of PCA % The covariance matrix for the data expressed with respect to the basis U % should be a diagonal matrix with non-zero entries only along the main % diagonal. We will verify this here. % Write code to compute the covariance matrix, covar. % When visualised as an image, you should see a straight line across the % diagonal (non-zero entries) against a blue background (zero entries).% -------------------- YOUR CODE HERE -------------------- covar = zeros(size(x, 1)); % You need to compute this covar=x*x'./size(x,2); % Visualise the covariance matrix. You should see a line across the % diagonal against a blue background. figure('name','Visualisation of covariance matrix'); imagesc(covar);%%================================================================ %% Step 2: Find k, the number of components to retain % Write code to determine k, the number of components to retain in order % to retain at least 99% of the variance.% -------------------- YOUR CODE HERE -------------------- k = 0; % Set k accordingly [m,n]=size(s); res=diag(s)'*fliplr(tril(ones(m),0)) tmp=find(res > res(m)*0.01); k=length(tmp); %%================================================================ %% Step 3: Implement PCA with dimension reduction % Now that you have found k, you can reduce the dimension of the data by % discarding the remaining dimensions. In this way, you can represent the % data in k dimensions instead of the original 144, which will save you % computational time when running learning algorithms on the reduced % representation. % % Following the dimension reduction, invert the PCA transformation to produce % the matrix xHat, the dimension-reduced data with respect to the original basis. % Visualise the data and compare it to the raw data. You will observe that % there is little loss due to throwing away the principal components that % correspond to dimensions with low variation.% -------------------- YOUR CODE HERE -------------------- xHat = zeros(size(x)); % You need to compute this xRot = zeros(size(x)); xRot=u(:,1:k)'*x; xHat(1:k,:)=xRot(1:k,:); xHat=u*xHat;% Visualise the data, and compare it to the raw data % You should observe that the raw and processed data are of comparable quality. % For comparison, you may wish to generate a PCA reduced image which % retains only 90% of the variance.figure('name',['PCA processed images ',sprintf('(%d / %d dimensions)', k, size(x, 1)),'']); display_network(xHat(:,randsel)); figure('name','Raw images'); display_network(x(:,randsel));%%================================================================ %% Step 4a: Implement PCA with whitening and regularisation % Implement PCA with whitening and regularisation to produce the matrix % xPCAWhite. epsilon = 0.1; xPCAWhite = zeros(size(x)); xPCAWhite = diag(1./sqrt(diag(s(:,1:k))+epsilon))*xRot; % -------------------- YOUR CODE HERE -------------------- %%================================================================ %% Step 4b: Check your implementation of PCA whitening % Check your implementation of PCA whitening with and without regularisation. % PCA whitening without regularisation results a covariance matrix % that is equal to the identity matrix. PCA whitening with regularisation % results in a covariance matrix with diagonal entries starting close to % 1 and gradually becoming smaller. We will verify these properties here. % Write code to compute the covariance matrix, covar. % % Without regularisation (set epsilon to 0 or close to 0), % when visualised as an image, you should see a red line across the % diagonal (one entries) against a blue background (zero entries). % With regularisation, you should see a red line that slowly turns % blue across the diagonal, corresponding to the one entries slowly % becoming smaller.% -------------------- YOUR CODE HERE -------------------- % Visualise the covariance matrix. You should see a red line across the % diagonal against a blue background. figure('name','Visualisation of covariance matrix'); imagesc(covar);%%================================================================ %% Step 5: Implement ZCA whitening % Now implement ZCA whitening to produce the matrix xZCAWhite. % Visualise the data and compare it to the raw data. You should observe % that whitening results in, among other things, enhanced edges.xZCAWhite = zeros(size(x));% -------------------- YOUR CODE HERE -------------------- xZCAWhite = u(:,1:k)*xPCAWhite; % Visualise the data, and compare it to the raw data. % You should observe that the whitened images have enhanced edges. figure('name','ZCA whitened images'); display_network(xZCAWhite(:,randsel)); figure('name','Raw images'); display_network(x(:,randsel));接下是幾幅圖片

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