Matrix Completion with Noise

Matrix Completion with Noise

18 Mar 2009 | Emmanuel J. Candès and Yaniv Plan
This paper explores the field of matrix completion, which addresses the recovery of a data matrix from incomplete or corrupted information. The authors survey recent literature showing that under suitable conditions, an unknown low-rank matrix can be recovered from a nearly minimal set of entries by solving a convex optimization problem, specifically nuclear-norm minimization subject to data constraints. They introduce novel results demonstrating that matrix completion is provably accurate even when the observed entries are corrupted with noise. The paper provides theoretical guarantees and numerical experiments to support these findings, highlighting the practical applicability of matrix completion in various fields such as collaborative filtering, system identification, global positioning, and remote sensing. The authors also discuss the relationship between matrix completion and compressed sensing, noting that while matrix completion does not satisfy the restricted isometry property (RIP) like compressed sensing, it still achieves robust recovery under certain conditions.This paper explores the field of matrix completion, which addresses the recovery of a data matrix from incomplete or corrupted information. The authors survey recent literature showing that under suitable conditions, an unknown low-rank matrix can be recovered from a nearly minimal set of entries by solving a convex optimization problem, specifically nuclear-norm minimization subject to data constraints. They introduce novel results demonstrating that matrix completion is provably accurate even when the observed entries are corrupted with noise. The paper provides theoretical guarantees and numerical experiments to support these findings, highlighting the practical applicability of matrix completion in various fields such as collaborative filtering, system identification, global positioning, and remote sensing. The authors also discuss the relationship between matrix completion and compressed sensing, noting that while matrix completion does not satisfy the restricted isometry property (RIP) like compressed sensing, it still achieves robust recovery under certain conditions.
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[slides and audio] Matrix Completion With Noise