Principal Component Analysis (PCA)
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Transcript of Principal Component Analysis (PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Principal Component Analysis Principal Component Analysis (PCA)(PCA)
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Alternative Derivation Alternative Derivation (PCA)(PCA)
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Alternative Derivation Alternative Derivation (PCA)(PCA)
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Alternative Derivation Alternative Derivation (PCA)(PCA)
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Alternative Derivation Alternative Derivation (PCA)(PCA)
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Singular Value DecompositionSingular Value Decomposition
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Singular Value DecompositionSingular Value Decomposition
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Singular Value DecompositionSingular Value Decomposition
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Example 1Example 1• Use the data set "noisy.mat" available on
your CD. The data set consists of 1965, 20-pixel-by-28-pixel grey-scale images distorted by adding Gaussian noises to each pixel with s=25.
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Example 1Example 1• Apply PCA to the noisy data. Suppose the
intrinsic dimensionality of the data is 10. Compute reconstructed images using the top d = 10 eigenvectors and plot original and reconstructed images
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Example 1Example 1• If original images are stored in matrix X (it is 560
by 1965 matrix) and reconstructed images are in matrix X_hat , you can type in
• colormap gray and then• imagesc(reshape(X(:, 10), 20 28)’)• imagesc(reshape(X_hat(:, 10), 20 28)’)to plot the 10th original image and its
reconstruction.
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Example 2Example 2
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Example 2Example 2• Load the sample data, which includes digits 2 and 3 of64 measurements on a sample of 400. load 2_3.mat
• Extract appropriate features by PCA
[u s v]=svd(X','econ');
• Create data
Low_dimensional_data=u(:,1:2);• Observe low dimensional dataImagesc(Low_dimensional_data)
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