Practical sketching algorithms for low-rank matrix approximation

TL;DR

This paper introduces simple, accurate, and stable sketching algorithms for low-rank matrix approximation that preserve structural properties and provide error bounds, supported by numerical experiments.

Contribution

It presents a suite of novel sketching algorithms that are easy to implement, provably correct, and capable of producing structured low-rank approximations with error guarantees.

Findings

Algorithms are simple, accurate, and numerically stable.

Methods can preserve structural properties like positive-semidefiniteness.

Numerical experiments confirm theoretical error bounds.

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.