Large-scale convex minimization with a low-rank constraint

Shai Shalev-Shwartz*, Alon Gonen, Ohad Shamir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

85 Scopus citations

Abstract

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left and right singular vectors corresponding to the largest singular value of a certain matrix, which can be calculated in linear time. This leads to an algorithm which can scale to large matrices arising in several applications such as matrix completion for collaborative filtering and robust low rank matrix approximation.

Original languageAmerican English
Title of host publicationProceedings of the 28th International Conference on Machine Learning, ICML 2011
Pages329-336
Number of pages8
StatePublished - 2011
Event28th International Conference on Machine Learning, ICML 2011 - Bellevue, WA, United States
Duration: 28 Jun 20112 Jul 2011

Publication series

NameProceedings of the 28th International Conference on Machine Learning, ICML 2011

Conference

Conference28th International Conference on Machine Learning, ICML 2011
Country/TerritoryUnited States
CityBellevue, WA
Period28/06/112/07/11

Fingerprint

Dive into the research topics of 'Large-scale convex minimization with a low-rank constraint'. Together they form a unique fingerprint.

Cite this