sklearn.utils.extmath.randomized_range_finder

sklearn.utils.extmath.randomized_range_finder(A, size, n_iter, power_iteration_normalizer='auto', random_state=None)

Computes an orthonormal matrix whose range approximates the range of A.

Parameters:

A : 2D array

The input data matrix

size : integer

Size of the return array

n_iter : integer

Number of power iterations used to stabilize the result

power_iteration_normalizer : ‘auto’ (default), ‘QR’, ‘LU’, ‘none’

Whether the power iterations are normalized with step-by-step QR factorization (the slowest but most accurate), ‘none’ (the fastest but numerically unstable when n_iter is large, e.g. typically 5 or larger), or ‘LU’ factorization (numerically stable but can lose slightly in accuracy). The ‘auto’ mode applies no normalization if n_iter <= 2 and switches to LU otherwise.

New in version 0.18.

random_state : int, RandomState instance or None, optional (default=None)

The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Returns:

Q : 2D array

A (size x size) projection matrix, the range of which approximates well the range of the input matrix A.

Notes

Follows Algorithm 4.3 of Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions Halko, et al., 2009 (arXiv:909) https://arxiv.org/pdf/0909.4061.pdf

An implementation of a randomized algorithm for principal component analysis A. Szlam et al. 2014