[PCA]

- minor improvements

git-svn-id: http://moon:8086/svn/matlab/trunk@95 801c6759-fa7c-4059-a304-17956f83a07c

RBM/UFLDL/common/loadMNISTImages.m

@@ -14,6 +14,7 @@ numCols = fread(fp, 1, 'int32', 0, 'ieee-be');
 
 images = fread(fp, inf, 'unsigned char');
 images = reshape(images, numCols, numRows, numImages);
+%images = images(:,:, 1:200);
 images = permute(images,[2 1 3]);
 
 fclose(fp);

RBM/mnist_gen_pca.m

@@ -17,7 +17,7 @@ avg = mean(x, 1);     % Compute the mean pixel intensity value separately for ea
 x = x - repmat(avg, size(x, 1), 1);
 
 fprintf('Do the PCA whitening\n');
-[xHat, k, xZCAWhite] = pca(x, retained_variance_target);
+[xHat, k, xZCAWhite, xPCAWhite] = pca(x, retained_variance_target);
 
 figure('name',['PCA processed images ',sprintf('(%d / %d dimensions)', k, size(x, 1)),'']);
 display_network(xHat(:,randsel));

RBM/pca.m

@@ -5,7 +5,8 @@
 %  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)
+function [xHat, k, xZCAWhite, xPCAWhite] = pca(x, retained_variance_target)
+epsilon = 1e-1; 
 
 %%================================================================
 %% Step 1a: Implement PCA to obtain xRot
@@ -19,8 +20,8 @@ fprintf('Perform Singular Value Decomposition\n');
 [U,S,V] = svd(sigma);
 
 fprintf('Perform PCA transformation\n');
-xrot = U' * x;
+wpca = U' * diag(sqrt(1./(diag(S) + epsilon)));
-
+wzca = U * wpca;
 %%================================================================
 %% Step 2: Find k, the number of components to retain
 %  Write code to determine k, the number of components to retain in order
@@ -51,6 +52,7 @@ k = k
 %  correspond to dimensions with low variation.
 
 fprintf('Calculate xHat\n');
+xrot = U' * x;
 xHat = U(:, 1:k) * xrot(1:k, :);
 
 %%================================================================
@@ -58,10 +60,9 @@ xHat = U(:, 1:k) * xrot(1:k, :);
 %  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;
+xPCAWhite = wpca * x;
 
 %%================================================================
 %% Step 5: Implement ZCA whitening
@@ -71,5 +72,5 @@ xPCAWhite = diag(sqrt(1./(diag(S) + epsilon))) * xrot;
 
 %%% YOUR CODE HERE %%%
 fprintf('Calculate xZCAWhite\n');
-xZCAWhite = U * xPCAWhite;
+xZCAWhite = wzca * x;
 

RBM/pca_eval.asv

@@ -7,8 +7,8 @@ Ndim = 2;
 K = 1;
 epsilon = 0.1;
 
-x = 2*(rand(Ndim, Ntrain)-0.5)
+x = 2*(rand(Ndim, Ntrain)-0.5);
-x = 0.3*x + repmat(linspace(-0.7,0.7, Ntrain), Ndim, 1)
+x = 0.3*x + repmat(linspace(-0.7,0.7, Ntrain), Ndim, 1);
 plot(x(1,:), x(2,:), '+'); axis([-1 1 -1 1]); grid; title('Raw data'); xlabel('x_1'); ylabel('x_2');
 
 sigma = x * x' / size(x, 2)
@@ -17,20 +17,27 @@ xrot = U' * x;
 figure;
 plot(xrot(1,:), xrot(2,:), '+'); axis([-1 1 -1 1]); grid; title('Rotated data'); xlabel('x_{rot,1}'); ylabel('x_{rot,2}');
 
-lambda = diag(S);
+xpca = pcdiag(sqrt(1./(diag(S) + epsilon))) * xrot;
-retained_variance = sum(lambda(1:K))./sum(lambda)
-
-xpca = diag(sqrt(1./(lambda + epsilon))) * xrot;
 figure;
 plot(xpca(1,:), xpca(2,:), '+'); axis([-1 1 -1 1]); grid; title('Whitened data dim=2'); xlabel('x_{pca,1}'); ylabel('x_{pca,2}');
 
+
 xtilde = zeros(size(xrot));
 xtilde(1:K, :) = xrot(1:K, :);
 
+lambda = diag(S);
+retained_variance = sum(lambda(1:K))./sum(lambda)
+
 figure;
 plot(xtilde(1,:), xtilde(2,:), '+'); axis([-1 1 -1 1]); grid; title('Rotated data reduced to dim = 1'); xlabel('x_{tilde,1}'); ylabel('x_{tilde,2}');
 
-xhat = U*xtilde;
+size (U)
+size(xrot)
+xhat = U(:, 1:K) * xrot(1:K, :);
 
 figure;
 plot(xhat(1,:), xhat(2,:), '+'); axis([-1 1 -1 1]); grid; title('Data reduced to dim = 1'); xlabel('x_{hat,1}'); ylabel('x_{hat,2}');
+
+xpca1 = diag(sqrt(1./(diag(S)))) * xhat;
+figure;
+plot(xpca1(1,:), xpca1(2,:), '+'); axis([-1 1 -1 1]); grid; title('Whitened data dim=1'); xlabel('x_{pca,1}'); ylabel('x_{pca,2}');