☆ 4.5 Article

Low-Rank Matrix Recovery From Errors and Erasures

IEEE TRANSACTIONS ON INFORMATION THEORY (2013)

期刊

IEEE TRANSACTIONS ON INFORMATION THEORY

卷 59, 期 7, 页码 4324-4337

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

DOI: 10.1109/TIT.2013.2249572

关键词

Low-rank; matrix decomposition; robustness; sparsity; statistical learning

类别

Computer Science, Information Systems Engineering, Electrical & Electronic

资金

National Science Foundation (NSF) [EFRI-0735905, EECS-1056028]
Defense Threat Reduction Agency [HDTRA 1-08-002]
NSF [0954059, 1017525]
Directorate For Engineering
Div Of Electrical, Commun & Cyber Sys [1056028] Funding Source: National Science Foundation
Division Of Computer and Network Systems
Direct For Computer & Info Scie & Enginr [0954059] Funding Source: National Science Foundation
Div Of Information & Intelligent Systems
Direct For Computer & Info Scie & Enginr [1017525] Funding Source: National Science Foundation

向作者/读者索取更多资源

Protocol

Reagent

摘要

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both 1) erasures, most entries are not observed, and 2) errors, values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when minimizing nuclear norm plus norm succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. By specializing this one single result in different ways, we recover (up to poly-log factors) as corollaries all the existing results in exact matrix completion, and exact sparse and low-rank matrix decomposition. Our unified result also provides the first guarantees for 1) recovery when we observe a vanishing fraction of entries of a corrupted matrix, and 2) deterministic matrix completion.

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