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Article: A perturbation inequality for concave functions of singular values and its applications in low-rank matrix recovery
Title | A perturbation inequality for concave functions of singular values and its applications in low-rank matrix recovery |
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Authors | |
Keywords | Exact and robust recovery Low-rank matrix recovery Schatten quasi-norm Singular value perturbation inequality |
Issue Date | 2016 |
Citation | Applied and Computational Harmonic Analysis, 2016, v. 40, n. 2, p. 396-416 How to Cite? |
Abstract | In this paper, we establish the following perturbation result concerning the singular values of a matrix: Let A,B,E Rm×n be given matrices, and let f:R+→R+ be a concave function satisfying f(0)=0. Then, we have min{m,n}Σi=1| (σi(A))-(σi(B)) ≤min{m,n}i=1(σi(A-B)) where ;bsubi;(.) denotes the i-th largest singular value of a matrix. This answers an open question that is of interest to both the compressive sensing and linear algebra communities. In particular, by taking f(.)=;(.)p; for any p∈(0,1], we obtain a perturbation inequality for the so-called Schatten p-quasi-norm, which allows us to confirm the validity of a number of previously conjectured conditions for the recovery of low-rank matrices via the popular Schatten p-quasi-norm heuristic. We believe that our result will find further applications, especially in the study of low-rank matrix recovery. |
Persistent Identifier | http://hdl.handle.net/10722/313608 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 2.231 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Yue, Man Chung | - |
dc.contributor.author | So, Anthony Man Cho | - |
dc.date.accessioned | 2022-06-23T01:18:44Z | - |
dc.date.available | 2022-06-23T01:18:44Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Applied and Computational Harmonic Analysis, 2016, v. 40, n. 2, p. 396-416 | - |
dc.identifier.issn | 1063-5203 | - |
dc.identifier.uri | http://hdl.handle.net/10722/313608 | - |
dc.description.abstract | In this paper, we establish the following perturbation result concerning the singular values of a matrix: Let A,B,E Rm×n be given matrices, and let f:R+→R+ be a concave function satisfying f(0)=0. Then, we have min{m,n}Σi=1| (σi(A))-(σi(B)) ≤min{m,n}i=1(σi(A-B)) where ;bsubi;(.) denotes the i-th largest singular value of a matrix. This answers an open question that is of interest to both the compressive sensing and linear algebra communities. In particular, by taking f(.)=;(.)p; for any p∈(0,1], we obtain a perturbation inequality for the so-called Schatten p-quasi-norm, which allows us to confirm the validity of a number of previously conjectured conditions for the recovery of low-rank matrices via the popular Schatten p-quasi-norm heuristic. We believe that our result will find further applications, especially in the study of low-rank matrix recovery. | - |
dc.language | eng | - |
dc.relation.ispartof | Applied and Computational Harmonic Analysis | - |
dc.subject | Exact and robust recovery | - |
dc.subject | Low-rank matrix recovery | - |
dc.subject | Schatten quasi-norm | - |
dc.subject | Singular value perturbation inequality | - |
dc.title | A perturbation inequality for concave functions of singular values and its applications in low-rank matrix recovery | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.acha.2015.06.006 | - |
dc.identifier.scopus | eid_2-s2.0-84953635310 | - |
dc.identifier.volume | 40 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 396 | - |
dc.identifier.epage | 416 | - |
dc.identifier.eissn | 1096-603X | - |
dc.identifier.isi | WOS:000368317100008 | - |