Hands-On Unsupervised Learning with Python

Whitening

An important application of the SVD is the whitening procedure, which forces the dataset, X, with a null mean (that is, E[X] = 0 or zero-centered), to have an identity covariance matrix, C, (which is real and symmetric). This method is extremely helpful, to improve the performance of many supervised algorithms, which can benefit from a uniform single variance shared by all components.

Applying the decomposition to C, we obtain the following:

The columns of the matrix V are the eigenvectors of C, while Λ is a diagonal matrix containing the eigenvalues (remember that the SVD outputs singular values, which are the square roots of the ...