Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Matrix completion via an alternating direction method

Language

English

Abstract

The matrix completion problem is to complete an unknown matrix from a small number of entries, and it captures many applications in diversified areas. Recently, it was shown that completing a low-rank matrix can be successfully accomplished by solving its convex relaxation problem using the nuclear norm. This paper shows that the alternating direction method (ADM) is applicable for completing a low-rank matrix including the noiseless case, the noisy case and the positive semidefinite case. The ADM approach for the matrix completion problem is easily implementable and very efficient. Numerical comparisons of the ADM approach with some state-of-the-art methods are reported. © 2011 The author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rightss reserved.

Keywords

alternating direction method, convex programming, low rank, matrix completion, noise, nuclear norm

Publication Date

2012

Source Publication Title

IMA Journal of Numerical Analysis

Volume

32

Issue

1

Start Page

227

End Page

245

Publisher

Oxford University Press

DOI

10.1093/imanum/drq039

Link to Publisher's Edition

http://dx.doi.org/10.1093/imanum/drq039

ISSN (print)

02724979

ISSN (electronic)

14643642

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