Improving Low-Rank Matrix Completion with Self-Expressiveness

Abstract

In this paper, we improve the low-rank matrix completion algorithm by assuming that the data points lie in a union of low dimensional subspaces. We applied the self-expressiveness, which is a property of a dataset when the data points lie in a union of low dimensional subspaces, to the low-rank matrix completion. By considering self-expressiveness of low dimensional subspaces, the proposed low-rank matrix completion may perform well even with little information, leading to the robust completion on a dataset with high missing rate. In our experiments on movie rating datasets, the proposed model outperforms state-of-the-art matrix completion models. In clustering experiments conducted on MNIST dataset, the result indicates that our method closely recovers the subspaces of original dataset even with the high missing rate.