whitening

Data matrix $X$ shape $(D, N)$. Zero mean centering or not depending on circumstance.

Compute eigen vectors with SVD:

$$U, S, V = \texttt{linalg.svd}(X)$$

Projection:

$$X' = U^\intercal*X$$

PCA whitening:

$$X_{\text{PCA} }=\texttt{diag}\left(\frac{1}{\texttt{diag}(\sqrt{S})+\epsilon}\right)*X'$$

ZCA whitening:

$$X_{\text{ZCA}}=U*X_{\text{PCA}}$$