PRACTICAL SKETCHING ALGORITHMS FOR LOW-RANK MATRIX APPROXIMATION

被引：110

作者：

Tropp, Joel A. ^{[1
]}

Yurtsever, Alp ^{[2
]}

Udell, Madeleine ^{[3
]}

Cevher, Volkan ^{[2
]}

机构：

[1] CALTECH, Comp & Math Sci, Pasadena, CA 91125 USA

[2] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland

[3] Cornell Univ, Ithaca, NY 14853 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2017年 / 38卷 / 04期

关键词：

dimension reduction; matrix approximation; numerical linear algebra; randomized algorithm; single-pass algorithm; sketching; streaming algorithm; subspace embedding; DIMENSIONALITY REDUCTION; RANDOMIZED ALGORITHM; LINEAR ALGEBRA;

D O I：

10.1137/17M1111590

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image, or sketch, of the matrix. 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.

引用

页码：1454 / 1485

页数：32

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