Matrix Completion from Noisy Entries

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 in [KMO09], 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.

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Raghunandan H. Keshavan, Andrea Montanari, Sewoong Oh
• Keywords: JMLR 2010, Low Complexity Algorithm, Noisy Observations, Random Subset