What is the difference between PCA solutions?

Hi, all

I am looking into two solutions of PCA(Principal Component Analysis), which are covariance matrix and singular value decomposition.

These two solutions are ran on the same dataset, but the resulting components are not the same.

The plot shows that the angle between a pair of corresponding components with high variance (first 3 components) are nearly the same with the angle is around 160 degrees. But the component pairs with low variance are perpendicular to each other.

May I know if this is normal? If it is normal, may I know the reason?

Thank you very much in advance. I look forward to hearing from you.

Best regards Wenlong

Answer 1

[Peter Perkins]

You haven't provided a lot of information about what you are actually doing.

If you are using the PRINCOMP function in the Statistics Toolbox, it uses the SVD function. But as is standard in PCA, if first centers the data. It also enforces a sign convention on the components so that the largest loading in each is positive.

If you called SVD, you may or may not have done either of those things. In other words, SVD is a numerical linear algebra function that is the computational basis for PCA, but lacks any of the "context". PRINCOMP is a function that does PCA.