Matrix Completion from Noisy Entries
Machine Learning
2012-04-10 v2 Machine Learning
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.
Cite
@article{arxiv.0906.2027,
title = {Matrix Completion from Noisy Entries},
author = {Raghunandan H. Keshavan and Andrea Montanari and Sewoong Oh},
journal= {arXiv preprint arXiv:0906.2027},
year = {2012}
}
Comments
22 pages, 3 figures