Riemannian Pursuit for Big Matrix Recovery

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Mingkui Tan, Ivor W. Tsang, Li Wang, Bart Vandereycken, Sinno Jialin Pan ;
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1539-1547, 2014.

Abstract

Low rank matrix recovery is a fundamental task in many real-world applications. The performance of existing methods, however, deteriorates significantly when applied to ill-conditioned or large-scale matrices. In this paper, we therefore propose an efficient method, called Riemannian Pursuit (RP), that aims to address these two problems simultaneously. Our method consists of a sequence of fixed-rank optimization problems. Each subproblem, solved by a nonlinear Riemannian conjugate gradient method, aims to correct the solution in the most important subspace of increasing size. Theoretically, RP converges linearly under mild conditions and experimental results show that it substantially outperforms existing methods when applied to large-scale and ill-conditioned matrices.

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