Factor and Component Analysis esp. Principal Component Analysis (PCA)
Principal Component Analysis (PCA)
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Principal Component Principal Component Analysis (PCA) Analysis (PCA)
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Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). Principal Component Analysis (PCA). - PowerPoint PPT Presentation
Transcript of Principal Component Analysis (PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Principal Component Analysis Principal Component Analysis (PCA)(PCA)
Alternative Derivation Alternative Derivation (PCA)(PCA)
Alternative Derivation Alternative Derivation (PCA)(PCA)
Alternative Derivation Alternative Derivation (PCA)(PCA)
Alternative Derivation Alternative Derivation (PCA)(PCA)
Singular Value DecompositionSingular Value Decomposition
Singular Value DecompositionSingular Value Decomposition
Singular Value DecompositionSingular Value Decomposition
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.
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
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.
Example 2Example 2
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)
