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崇左网站建设公司,学院网站建设的要求,wordpress网站攻击,社交网站设计自然图片的PCA白化 在这个练习里面我们将实现PCA和ZCA白化。首先先下载这个文件pca_exercise.zip, 然后我们解压它#xff0c;并用matlab打开它#xff0c;我们只需要更改pca_gen.m.这个文件。 然后把代码改成下面这个形式 %% %% Step 0a: Load data % Here we provide th…自然图片的PCA白化 在这个练习里面我们将实现PCA和ZCA白化。首先先下载这个文件pca_exercise.zip, 然后我们解压它并用matlab打开它我们只需要更改pca_gen.m.这个文件。 然后把代码改成下面这个形式 %% %% 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 -------------------- xx-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); xRotu*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 covarx*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); resdiag(s)*fliplr(tril(ones(m),0)) tmpfind(res res(m)*0.01); klength(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)); xRotu(:,1:k)*x; xHat(1:k,:)xRot(1:k,:); xHatu*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));接下是几幅图片
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