Robust Recovery of Corrupted Low-RankMatrix by Implicit Regularizers
Low-rank matrix recovery algorithms aim to recover a corrupted low-rank matrix with sparse errors. However, corrupted errors may not be sparse in real-world problems and the relationship between ℓ1 regularizer on noise and robust M-estimators is still unknown. This paper proposes a general robust fr...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 36(2014), 4 vom: 01. Apr., Seite 770-83 |
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| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2014
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | Low-rank matrix recovery algorithms aim to recover a corrupted low-rank matrix with sparse errors. However, corrupted errors may not be sparse in real-world problems and the relationship between ℓ1 regularizer on noise and robust M-estimators is still unknown. This paper proposes a general robust framework for low-rank matrix recovery via implicit regularizers of robust M-estimators, which are derived from convex conjugacy and can be used to model arbitrarily corrupted errors. Based on the additive form of half-quadratic optimization, proximity operators of implicit regularizers are developed such that both low-rank structure and corrupted errors can be alternately recovered. In particular, the dual relationship between the absolute function in ℓ1 regularizer and Huber M-estimator is studied, which establishes a connection between robust low-rank matrix recovery methods and M-estimators based robust principal component analysis methods. Extensive experiments on synthetic and real-world data sets corroborate our claims and verify the robustness of the proposed framework |
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| Beschreibung: | Date Completed 27.11.2015 Date Revised 10.09.2015 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2013.188 |