Riemannian Pursuit for Big Matrix Recovery

Greedy algorithm for nuclear norm minimization on the manifold (hopefully we'll get to see an implementation of it at some point in time)

Riemannian Pursuit for Big Matrix Recovery by Mingkui Tan, Ivor W. Tsang, Li Wang, Jialin Pan, Bart Vandereycken 

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.

Supplementary material


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