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arXiv · 0906.2027

Matrix Completion from Noisy Entries

Raghunandan H. Keshavan·Andrea Montanari·Sewoong Oh
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Abstract

Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan et al.(2009), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances.

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Raghunandan H. Keshavan, Andrea Montanari, Sewoong Oh. 2012-04-09. Matrix Completion from Noisy Entries. https://arxiv.org/abs/0906.2027

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