# sklearn.utils.extmath.randomized_svd¶

sklearn.utils.extmath.randomized_svd(M, n_components, n_oversamples=10, n_iter=’auto’, power_iteration_normalizer=’auto’, transpose=’auto’, flip_sign=True, random_state=0)[source]

Computes a truncated randomized SVD

Parameters: M : ndarray or sparse matrix Matrix to decompose n_components : int Number of singular values and vectors to extract. n_oversamples : int (default is 10) Additional number of random vectors to sample the range of M so as to ensure proper conditioning. The total number of random vectors used to find the range of M is n_components + n_oversamples. Smaller number can improve speed but can negatively impact the quality of approximation of singular vectors and singular values. n_iter : int or ‘auto’ (default is ‘auto’) Number of power iterations. It can be used to deal with very noisy problems. When ‘auto’, it is set to 4, unless n_components is small (< .1 * min(X.shape)) n_iter in which case is set to 7. This improves precision with few components. Changed in version 0.18. 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. transpose : True, False or ‘auto’ (default) Whether the algorithm should be applied to M.T instead of M. The result should approximately be the same. The ‘auto’ mode will trigger the transposition if M.shape[1] > M.shape[0] since this implementation of randomized SVD tend to be a little faster in that case. Changed in version 0.18. flip_sign : boolean, (True by default) The output of a singular value decomposition is only unique up to a permutation of the signs of the singular vectors. If flip_sign is set to True, the sign ambiguity is resolved by making the largest loadings for each component in the left singular vectors positive. 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.

Notes

This algorithm finds a (usually very good) approximate truncated singular value decomposition using randomization to speed up the computations. It is particularly fast on large matrices on which you wish to extract only a small number of components. In order to obtain further speed up, n_iter can be set <=2 (at the cost of loss of precision).

References

• Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions Halko, et al., 2009 http://arxiv.org/abs/arXiv:0909.4061
• A randomized algorithm for the decomposition of matrices Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert
• An implementation of a randomized algorithm for principal component analysis A. Szlam et al. 2014