recitation-pca - Recitation 10-701/15-781, Fall 2008 PCA By...

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Recitation 10-701/15-781, Fall 2008 PCA By Hanghang Tong (htong@cs) Some Parts of the slides are from previous years’ recitation and lecture notes 1
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Roadmap PCA: Maximize projected variance PCA: Minimize re-construction error PCA vs. SVD PCA vs. Feature Selection Kernel PCA 2
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PCA: Settings We have N data points in D dimension space, we want to project them into some low-dimensional space 3 2 x X 1 X 2 X 3 X 4 X 5 Here, N=5; D=2; and d=1 u ~ ~ ~ ~ 1 x X 1 ~ X 2 X 3 X 4 X 5 Q: How shall we select u (the projection direction)?
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PCA: Maximize the variance Q: How to choose (u)? A: Maximize the variance among red points? 4 2 x X 1 X 2 X 3 X 4 X 5 u ~ ~ ~ ~ 1 x X 1 ~ X 2 X 3 X 4 X 5
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Maximize Variance: (d=1) 2 x X 1 X 2 X 3 X 4 X 5 u ~ ~ ~ ~ 1 x X 1 ~ X 2 X 3 X 4 X 5 2 2 2 2 2 1 2 3 4 5 ( ) ( ) ( ) ( ) ( ) 5 X X X X X X X X X X the variance among red points = 1 2 3 4 5 1 2 3 4 5 ( 1,.
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recitation-pca - Recitation 10-701/15-781, Fall 2008 PCA By...

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