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Yes, this is a well known problem with PCA. So often we just whiten (http://en.wikipedia.org/wiki/Whitening_transformation http://en.wikipedia.org/wiki/Whiteni
by cf 13y ago
Yes, this is a well known problem with PCA. So often we just whiten (http://en.wikipedia.org/wiki/Whitening_transformation http://en.wikipedia.org/wiki/Whitening_transformation) the data first.
- deleted 13y ago[deleted]
- tgflynn 13y agoWhitening and (full rank) PCA use the same linear transformation except whitening scales the eigenvalues so all axes in the transformed system have unit variance. In other words whitening the data before applying PCA should result in the same eigenvectors expressed in the original coordinate system.
- cf 13y agoYes, but I think for many places where PCA is used, we are precisely interested in which eigenvectors have the largest eigenvalues. The scaling beforehand makes a unit change less likely to effect which eigenvectors are the most important.
- tgflynn 13y agoBut once you know the eigenvectors the eigenvalues (and hence their distribution) are determined, again in the original space. On the other hand if you're talking about the eigenvalues for the whitened data they're all 1. So I'm still not seeing what whitening adds to PCA. Just rescaling each dimension of the original space so that all dimensions have unit variance, without doing any rotations, may change things, but I don't think that's what is usually called whitening (according to Wikipedia).
- mturmon 13y agoYou are absolutely correct, and your interlocutor is mistaken to use a whitening transformation before PCA.