Convolutional neural networks(CNN) (五) PCA in 2D Exercise

{作为CNN学习入门的一部分，笔者在这里逐步给出UFLDL的各章节Exercise的个人代码实现，供大家参考指正}

理论部分可以在线参阅(页面最下方有中文选项)PCA到Implementing PCA/Whitening部分内容，

此次练习比较简单，只给出相应代码与结果：

pca_2d.m

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, :),'r');% 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%  You need to make sure that the data has been approximately zero-mean.x = bsxfun(@minus, x, mean(x,2));sigma = x * x' / size(x, 2);[U,S,V] = svd(sigma);u = U;% -------------------------------------------------------- % 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, :), 'b', 'filled');% 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 thisxRot = U' * x;          % rotated version of the data. % -------------------------------------------------------- % 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 thisxTilde = U(:,1:k)' * x; % reduced dimension representation of the data,                         % where k is the number of eigenvectors to keepxHat = U(:,1:k) * xTilde; % projecting the xRot back onto the original axes% -------------------------------------------------------- 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 thisxPCAWhite = 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 thisxZCAWhite = 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. :)

实验结果：

需要注意的是，在第一张图片中，实心圈点代表raw data而实心点代表zero-mean后的数据，之后的图也都是在zero-mean之后作出来的。