Practical sketching algorithms for low-rank matrix approximation
Numerical Analysis
2018-01-03 v2 Data Structures and Algorithms
Numerical Analysis
Computation
Machine Learning
Abstract
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.
Cite
@article{arxiv.1609.00048,
title = {Practical sketching algorithms for low-rank matrix approximation},
author = {Joel A. Tropp and Alp Yurtsever and Madeleine Udell and Volkan Cevher},
journal= {arXiv preprint arXiv:1609.00048},
year = {2018}
}