Matrix Completion Based on Low-Rank and Local Features Applied to Images Recovery and Recommendation Systems

Abstract

Recent advances have shown that the challenging problem of matrix completion arises from real-world applications, such as image recovery, and recommendation systems. Existing matrix completion methods utilize the low-rank property of sparse matrices to fill missing entries, which essentially exploits the low-rank relationship and ignores the local features of sparse matrices. In this paper, we propose a novel matrix completion method that takes the path of combining local features and low-rank information. First, the original sparse matrix is processed so that the neighboring rows and columns of the sparse matrix are most similar to each other, and then the missing data are filled by the iterative rank-one matrix completion method. Moreover, we use two-dimensional convolutional operations of sparse matrices to obtain the local features to dredge up the missing entries. Finally, the two filled results are integrated to obtain the final missing entries. We conduct extensive experiments on the real-world datasets. The experimental results demonstrate the significant outperforms of the proposed method on five image datasets of different sizes, and show a strong competitive advantage on the recommender system datasets.

Keywords

• Matrix completion
• image completion
• low-rank matrix
• image recovery
• recommendation systems