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Article: Matrix completion via an alternating direction method

TitleMatrix completion via an alternating direction method
Authors
Keywordslow rank
nuclear norm
alternating direction method
convex programming
matrix completion
noise
Issue Date2012
Citation
IMA Journal of Numerical Analysis, 2012, v. 32, n. 1, p. 227-245 How to Cite?
AbstractThe 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.
Persistent Identifierhttp://hdl.handle.net/10722/250994
ISSN
2020 Impact Factor: 2.601
2020 SCImago Journal Rankings: 1.672
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Caihua-
dc.contributor.authorHe, Bingsheng-
dc.contributor.authorYuan, Xiaoming-
dc.date.accessioned2018-02-01T01:54:17Z-
dc.date.available2018-02-01T01:54:17Z-
dc.date.issued2012-
dc.identifier.citationIMA Journal of Numerical Analysis, 2012, v. 32, n. 1, p. 227-245-
dc.identifier.issn0272-4979-
dc.identifier.urihttp://hdl.handle.net/10722/250994-
dc.description.abstractThe 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.-
dc.languageeng-
dc.relation.ispartofIMA Journal of Numerical Analysis-
dc.subjectlow rank-
dc.subjectnuclear norm-
dc.subjectalternating direction method-
dc.subjectconvex programming-
dc.subjectmatrix completion-
dc.subjectnoise-
dc.titleMatrix completion via an alternating direction method-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1093/imanum/drq039-
dc.identifier.scopuseid_2-s2.0-84863068818-
dc.identifier.volume32-
dc.identifier.issue1-
dc.identifier.spage227-
dc.identifier.epage245-
dc.identifier.eissn1464-3642-
dc.identifier.isiWOS:000299350400010-
dc.identifier.issnl0272-4979-

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