Fixed Point Iteration Algorithms for Low-rank Matrix Completion

Abstract

A lot of applications can be formulated as matrix completion problems. In order to address such problems, a common assumption is that the underlying matrix is (approximately) low-rank. Under certain conditions, the recovery of low-rank matrix can be done via nuclear norm minimization, a convex program. Scalable and fast algorithms are essential as the practical matrix completion tasks always occur on a large scale. Here we study two algorithms and generalize the uni ed framework of xed point iteration algorithm. We derive the convergence results and propose a new algorithm based on the insights. Compared with the baseline algorithms, our proposed method is signi cantly more e cient without loss of precision and acceleration potentiality. iii