Fast Monte-Carlo algorithms for finding low-rank approximations

Fast Monte-Carlo algorithms for finding low-rank approximations (1998)

by Alan Frieze , Ravi Kannan , Santosh Vempala

Venue:	IN PROCEEDINGS OF THE 39TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
Citations:	137 - 14 self

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Datum	Value	Source
TITLE	Fast Monte-Carlo algorithms for finding low-rank approximations	user correction
AUTHOR NAME	Alan Frieze	user correction
AUTHOR AFFIL	Carnegie Mellon University	user correction
AUTHOR NAME	Ravi Kannan	user correction
AUTHOR AFFIL	Yale University	user correction
AUTHOR NAME	Santosh Vempala	user correction
AUTHOR AFFIL	M. I. T.	user correction
ABSTRACT	We consider the problem of approximating a given m * n matrix A by another matrix of specified rank k, which is smaller than m and n. The Singular Value Decomposition (SVD) can be used to find the "best " such approximation. However, it takes time polynomial in m, n which is prohibitive for some modern applications. In this paper, we develop an algorithm which is qualitatively faster, provided we may sample the entries of the matrix according to a natural probability distribution. In many applications such sampling can be done efficiently. Our main result is a randomized algorithm to find the description of a matrix D * of rank at most k so that \|\|A- D*\|\|2F < = min D,rank(D)<=k \|\|A- D\|\|	SVM HeaderParse 0.2
YEAR	1998	INFERENCE
VENUE	IN PROCEEDINGS OF THE 39TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	370--378	INFERENCE
VOLUME	51	INFERENCE
CITATIONS	6 found	ParsCit 1.0