TY - GEN

T1 - Large-scale convex minimization with a low-rank constraint

AU - Shalev-Shwartz, Shai

AU - Gonen, Alon

AU - Shamir, Ohad

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053458764&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053458764

SN - 9781450306195

T3 - Proceedings of the 28th International Conference on Machine Learning, ICML 2011

SP - 329

EP - 336

BT - Proceedings of the 28th International Conference on Machine Learning, ICML 2011

T2 - 28th International Conference on Machine Learning, ICML 2011

Y2 - 28 June 2011 through 2 July 2011

ER -