Faq why does PCAENGINE change the sign of the loadings returned by SVD
Why does the PCAENGINE change the sign of the loadings returned by SVD?
A PCA model is ambiguous with regards to sign flips, i.e. if you have a set of scores
T and loads
P, the model
X = TP' is no more or less valid than the model
X = (-T)(-P'). Further complicating the matter is the fact that MATLAB's SVD routine, upon which our PCAENGINE is based, sometimes flips the signs of the scores and loadings when small changes are made in the data.
Because of this, we post-process the data so that the sign on the loads will make the elements as positive as possible. This aids interpretation. If you're looking at spectra, you'd rather see positive loads than negative!
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