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No. PCA tries to project to the subspace that preserves as much distance in the input space possible. If you multiply a coordinate in the input space by a fac
by robrenaud 14y ago
No.
PCA tries to project to the subspace that preserves as much distance in the input space possible. If you multiply a coordinate in the input space by a factor of 2, it will contribute relatively more to the distances, and hence change the fitted projection beyond just a scaling factor.
- binarysolo 14y agoThanks for the refresher, and a followup basic question: what methods are best at just ranking relative variance of each dimension/component regardless of unit scaling? SVDs, ? Edit: Ah right - http://en.wikipedia.org/wiki/Whitening_transformation http://en.wikipedia.org/wiki/Whitening_transformation
- thisrod 14y agoSo we're talking about a very general problem. When I noticed that a system of equations including x=y can have a different least-squares solution when you change it to 2x=2y, I was quite surprised.