jens
32063406bd
- minor improvements git-svn-id: http://moon:8086/svn/matlab/trunk@95 801c6759-fa7c-4059-a304-17956f83a07c
77 lines
3.0 KiB
Matlab
77 lines
3.0 KiB
Matlab
%%================================================================
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%% Step 0a: Load data
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% Here we provide the code to load natural image data into x.
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% x will be a 784 * 600000 matrix, where the kth column x(:, k) corresponds to
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% the raw image data from the kth 12x12 image patch sampled.
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% You do not need to change the code below.
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function [xHat, k, xZCAWhite, xPCAWhite] = pca(x, retained_variance_target)
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epsilon = 1e-1;
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%%================================================================
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%% Step 1a: Implement PCA to obtain xRot
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% Implement PCA to obtain xRot, the matrix in which the data is expressed
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% with respect to the eigenbasis of sigma, which is the matrix U.
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fprintf('Calculate covariance matrix of size %d x %d\n', size(x, 1), size(x, 1));
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sigma = x * x' / size(x, 2);
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fprintf('Perform Singular Value Decomposition\n');
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[U,S,V] = svd(sigma);
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fprintf('Perform PCA transformation\n');
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wpca = U' * diag(sqrt(1./(diag(S) + epsilon)));
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wzca = U * wpca;
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%%================================================================
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%% Step 2: Find k, the number of components to retain
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% Write code to determine k, the number of components to retain in order
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% to retain at least 99% of the variance.
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fprintf('Find K for variance target of %f\n', 100*retained_variance_target);
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retained_variance = 1.0;
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lambda = diag(S);
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k = length(lambda);
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while(retained_variance > retained_variance_target)
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retained_variance = sum(lambda(1:k))./sum(lambda);
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k = k - 1;
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end
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k = k
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%%================================================================
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%% Step 3: Implement PCA with dimension reduction
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% Now that you have found k, you can reduce the dimension of the data by
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% discarding the remaining dimensions. In this way, you can represent the
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% data in k dimensions instead of the original 144, which will save you
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% computational time when running learning algorithms on the reduced
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% representation.
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%
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% Following the dimension reduction, invert the PCA transformation to produce
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% the matrix xHat, the dimension-reduced data with respect to the original basis.
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% Visualise the data and compare it to the raw data. You will observe that
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% there is little loss due to throwing away the principal components that
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% correspond to dimensions with low variation.
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fprintf('Calculate xHat\n');
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xrot = U' * x;
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xHat = U(:, 1:k) * xrot(1:k, :);
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%%================================================================
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%% Step 4a: Implement PCA with whitening and regularisation
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% Implement PCA with whitening and regularisation to produce the matrix
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% xPCAWhite.
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%%% YOUR CODE HERE %%%
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fprintf('Calculate xPCAWhite\n');
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xPCAWhite = wpca * x;
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%%================================================================
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%% Step 5: Implement ZCA whitening
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% Now implement ZCA whitening to produce the matrix xZCAWhite.
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% Visualise the data and compare it to the raw data. You should observe
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% that whitening results in, among other things, enhanced edges.
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%%% YOUR CODE HERE %%%
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fprintf('Calculate xZCAWhite\n');
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xZCAWhite = wzca * x;
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