PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Large-Scale Convex Minimization with a Low-Rank Constraint
Shai Shalev-Shwartz, Alon Gonen and Ohad Shamir
In: ICML 2011, June 2011, Bellevue, Washington, USA.

Abstract

We address the problem of minimizing a con- vex function over the space of large matri- ces with low rank. While this optimization problem is hard in general, we propose an ef- cient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) nd- ing the left and right singular vectors cor- responding 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 comple- tion for collaborative ltering and robust low rank matrix approximation.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:8911
Deposited By:Shai Shalev-Shwartz
Deposited On:21 February 2012