Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Fast Algorithms for Approximating the Singular Value Decomposition

Fast Algorithms for Approximating the Singular Value Decomposition TKD00017 ACM (Typeset by SPi, Manila, Philippines) 1 of 36 February 22, 2011 Fast Algorithms for Approximating the Singular Value Decomposition ADITYA KRISHNA MENON and CHARLES ELKAN, University of California, San Diego A low-rank approximation to a matrix A is a matrix with signi cantly smaller rank than A, and which is close to A according to some norm. Many practical applications involving the use of large matrices focus on low-rank approximations. By reducing the rank or dimensionality of the data, we reduce the complexity of analyzing the data. The singular value decomposition is the most popular low-rank matrix approximation. However, due to its expensive computational requirements, it has often been considered intractable for practical applications involving massive data. Recent developments have tried to address this problem, with several methods proposed to approximate the decomposition with better asymptotic runtime. We present an empirical study of these techniques on a variety of dense and sparse datasets. We nd that a sampling approach of Drineas, Kannan and Mahoney is often, but not always, the best performing method. This method gives solutions with high accuracy much faster than classical SVD algorithms, on large sparse datasets in particular. Other modern methods, such http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Knowledge Discovery from Data (TKDD) Association for Computing Machinery

Fast Algorithms for Approximating the Singular Value Decomposition

Download PDF
36 pages

Loading next page...
 
/lp/association-for-computing-machinery/fast-algorithms-for-approximating-the-singular-value-decomposition-M18bj7mzF8

References (45)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2011 by ACM Inc.
ISSN
1556-4681
DOI
10.1145/1921632.1921639
Publisher site
See Article on Publisher Site

Abstract

TKD00017 ACM (Typeset by SPi, Manila, Philippines) 1 of 36 February 22, 2011 Fast Algorithms for Approximating the Singular Value Decomposition ADITYA KRISHNA MENON and CHARLES ELKAN, University of California, San Diego A low-rank approximation to a matrix A is a matrix with signi cantly smaller rank than A, and which is close to A according to some norm. Many practical applications involving the use of large matrices focus on low-rank approximations. By reducing the rank or dimensionality of the data, we reduce the complexity of analyzing the data. The singular value decomposition is the most popular low-rank matrix approximation. However, due to its expensive computational requirements, it has often been considered intractable for practical applications involving massive data. Recent developments have tried to address this problem, with several methods proposed to approximate the decomposition with better asymptotic runtime. We present an empirical study of these techniques on a variety of dense and sparse datasets. We nd that a sampling approach of Drineas, Kannan and Mahoney is often, but not always, the best performing method. This method gives solutions with high accuracy much faster than classical SVD algorithms, on large sparse datasets in particular. Other modern methods, such

Journal

ACM Transactions on Knowledge Discovery from Data (TKDD) – Association for Computing Machinery

Published: Feb 1, 2011

There are no references for this article.