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- Publisher Website: 10.1145/1970392.1970395
- Scopus: eid_2-s2.0-79960675858
- WOS: WOS:000291246000003
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Conference Paper: Robust principal component analysis?
Title | Robust principal component analysis? |
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Authors | |
Keywords | Duality L -norm minimization 1 Low-rank matrices Nuclear-norm minimization Principal components Robustness vis-a-vis outliers Sparsity Video surveillance |
Issue Date | 2011 |
Citation | Journal of the ACM, 2011, v. 58, n. 3, article no. 11 How to Cite? |
Abstract | This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the l1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well.We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces. © 2011 ACM. |
Persistent Identifier | http://hdl.handle.net/10722/326871 |
ISSN | 2023 Impact Factor: 2.3 2023 SCImago Journal Rankings: 2.866 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Candès, Emmanuel J. | - |
dc.contributor.author | Li, Xiaodong | - |
dc.contributor.author | Ma, Yi | - |
dc.contributor.author | Wright, John | - |
dc.date.accessioned | 2023-03-31T05:27:08Z | - |
dc.date.available | 2023-03-31T05:27:08Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Journal of the ACM, 2011, v. 58, n. 3, article no. 11 | - |
dc.identifier.issn | 0004-5411 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326871 | - |
dc.description.abstract | This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the l1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well.We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces. © 2011 ACM. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of the ACM | - |
dc.subject | Duality | - |
dc.subject | L -norm minimization 1 | - |
dc.subject | Low-rank matrices | - |
dc.subject | Nuclear-norm minimization | - |
dc.subject | Principal components | - |
dc.subject | Robustness vis-a-vis outliers | - |
dc.subject | Sparsity | - |
dc.subject | Video surveillance | - |
dc.title | Robust principal component analysis? | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1145/1970392.1970395 | - |
dc.identifier.scopus | eid_2-s2.0-79960675858 | - |
dc.identifier.volume | 58 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | article no. 11 | - |
dc.identifier.epage | article no. 11 | - |
dc.identifier.eissn | 1557-735X | - |
dc.identifier.isi | WOS:000291246000003 | - |