jens
32063406bd
- minor improvements git-svn-id: http://moon:8086/svn/matlab/trunk@95 801c6759-fa7c-4059-a304-17956f83a07c
44 lines
1.3 KiB
Plaintext
44 lines
1.3 KiB
Plaintext
function pca_eval()
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close all;
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Ntrain = 100;
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Ndim = 2;
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K = 1;
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epsilon = 0.1;
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x = 2*(rand(Ndim, Ntrain)-0.5);
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x = 0.3*x + repmat(linspace(-0.7,0.7, Ntrain), Ndim, 1);
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plot(x(1,:), x(2,:), '+'); axis([-1 1 -1 1]); grid; title('Raw data'); xlabel('x_1'); ylabel('x_2');
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sigma = x * x' / size(x, 2)
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[U,S,V] = svd(sigma)
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xrot = U' * x;
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figure;
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plot(xrot(1,:), xrot(2,:), '+'); axis([-1 1 -1 1]); grid; title('Rotated data'); xlabel('x_{rot,1}'); ylabel('x_{rot,2}');
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xpca = pcdiag(sqrt(1./(diag(S) + epsilon))) * xrot;
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figure;
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plot(xpca(1,:), xpca(2,:), '+'); axis([-1 1 -1 1]); grid; title('Whitened data dim=2'); xlabel('x_{pca,1}'); ylabel('x_{pca,2}');
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xtilde = zeros(size(xrot));
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xtilde(1:K, :) = xrot(1:K, :);
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lambda = diag(S);
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retained_variance = sum(lambda(1:K))./sum(lambda)
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figure;
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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}');
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size (U)
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size(xrot)
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xhat = U(:, 1:K) * xrot(1:K, :);
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figure;
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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}');
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xpca1 = diag(sqrt(1./(diag(S)))) * xhat;
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figure;
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plot(xpca1(1,:), xpca1(2,:), '+'); axis([-1 1 -1 1]); grid; title('Whitened data dim=1'); xlabel('x_{pca,1}'); ylabel('x_{pca,2}');
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