[RBM]

- added

git-svn-id: http://moon:8086/svn/matlab/trunk@93 801c6759-fa7c-4059-a304-17956f83a07c

RBM/pca.m

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+%%================================================================
+%% Step 0a: Load data
+%  Here we provide the code to load natural image data into x.
+%  x will be a 784 * 600000 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.
+
+function [xHat, k, xZCAWhite] = pca(x, retained_variance_target)
+ 
+%%================================================================
+%% 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.
+
+fprintf('Calculate covariance matrix of size %d x %d\n', size(x, 1), size(x, 1));
+sigma = x * x' / size(x, 2);
+
+fprintf('Perform Singular Value Decomposition\n');
+[U,S,V] = svd(sigma);
+
+fprintf('Perform PCA transformation\n');
+xrot = U' * x;
+
+%%================================================================
+%% 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.
+
+fprintf('Find K for variance target of %f\n', 100*retained_variance_target);
+retained_variance = 1.0;
+lambda = diag(S);
+k = length(lambda);
+while(retained_variance > retained_variance_target)
+	retained_variance = sum(lambda(1:k))./sum(lambda);
+	k = k - 1;
+end
+k = k
+
+%%================================================================
+%% 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.
+
+fprintf('Calculate xHat\n');
+xHat = U(:, 1:k) * xrot(1:k, :);
+
+%%================================================================
+%% Step 4a: Implement PCA with whitening and regularisation
+%  Implement PCA with whitening and regularisation to produce the matrix
+%  xPCAWhite. 
+
+epsilon = 1e-1; 
+%%% YOUR CODE HERE %%%
+fprintf('Calculate xPCAWhite\n');
+xPCAWhite = diag(sqrt(1./(diag(S) + epsilon))) * xrot;
+
+%%================================================================
+%% 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.
+
+%%% YOUR CODE HERE %%%
+fprintf('Calculate xZCAWhite\n');
+xZCAWhite = U * xPCAWhite;
+