Visualizing SVD/PCA and applying to new data
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I have an SVD for a data set as U S V'. My data are images, but my questions will be general.
I know how to reduce the rank of the original data by zeroing out small singular values and computing U*S*V', but:
- I want to isolate one dimension of variance, say, the one corresponding to the n th largest eigenvalue. This should be some basis vector, right? How do I get that basis vector? I thought it would be the n th column of U*S, but it's not.
- How do I fit some new data that wasn't in the original set to the SVD's bases?
Thanks in advance.
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Chaman Sabharawal
2017-6-11
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Assuming your data matrix A is observation vs arrtibutes. You are reducing attrubutes. Both ways reduction standard A= USV^T or AV=US Reducing it on attributes only you get A reduced to AV. For Reducing on one dimension replace V with a desired direction vector. I hope this is what you are looking for. Chaman
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2017-1-16
2017-6-11
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