Get U, Sigma, V* matrix from Truncated SVD in scikit-learn

Question

I am using truncated SVD from scikit-learn package.

In the definition of SVD, an original matrix A is approxmated as a product A ≈ UΣV* where U and V have orthonormal columns, and Σ is non-negative diagonal.

I need to get the U, Σ and V* matrices.

Looking at the source code here I found out that V* is stored in self.components_ field after calling fit_transform.

Is it possible to get U and Σ matrices?

My code:

import sklearn.decomposition as skd
import numpy as np

matrix = np.random.random((20,20))
trsvd = skd.TruncatedSVD(n_components=15)
transformed = trsvd.fit_transform(matrix)
VT = trsvd.components_

Answer 1

Looking into the source via the link you provided, TruncatedSVD is basically a wrapper around sklearn.utils.extmath.randomized_svd; you can manually call this yourself like this:

from sklearn.utils.extmath import randomized_svd

U, Sigma, VT = randomized_svd(X, 
                              n_components=15,
                              n_iter=5,
                              random_state=None)