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Whitening and (full rank) PCA use the same linear transformation except whitening scales the eigenvalues so all axes in the transformed system have unit varianc
by tgflynn 14y ago
Whitening 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 14y 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 14y 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 14y agoYou are absolutely correct, and your interlocutor is mistaken to use a whitening transformation before PCA.