Work

Matrix Completion from Noisy Entries

Year: 2009

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.0906.2027

Authors: Keshavan, Raghunandan H., Montanari, Andrea, Oh, Sewoong

Institution: Stanford University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Samsung

Awards: G6671297155, Mean field asymptotic for stochastic processes on graphs, CAREER: New Information Processing Techniques from Statistical Physics and Probability Theory

OpenAlex ID: W2136015602

Cites: 25

Cited by: 294

Related to: 20