TobiLang
commented
4 years ago PCA preparation consists of two steps:
- Substract the mean per dimension. The resulting data has mean Zero. This is done to avoid numerical difficulties
- Divide each dimension by its standard deviation. Now, the data is unit-free, has a variance of 1 but leaves the correlations between dimensions intact.
In PCA, the principal components are the n-Eigenvectors with the largest Eigenvalues. This can be done either by:
- Hands-On the covariance matrix:
- Compute the data covariance matrix.
- Compute the Eigenvalues and Eigenvectors of the covariance matrix.
- Select the Eigenvectors with the largest Eigenvalues.
- Via SVD, because it just computes and orders the desired Eigenvectors for you (as you already stated in your comment).
I have a question, why are you applying a SVD on a zero-mean (along the first axis) matrix? I'm not sure that's correct, I think you need to apply the SVD to the covariance matrix. In fact, when checking the pca.explained_varianceratio, that corresponds only to component of the vector S returned by the SVD (normalized to the sum of elements in the vector) applied on a covariance matrix.