Hybrid Matrix Completion Model for Improved Images Recovery and Recommendation Systems

Matrix completion methods have been widely applied in images recovery and recommendation systems. Most of them are only based on the low-rank characteristics of matrices to predict the missing entries. However, these methods lack consideration of local information. To further improve the performance of matrix completion. In this paper, we propose a novel model based on matrix decompositions and matrix local information. Specifically, we update a number of rank-one matrices, which circumvented the rank estimation in matrix decomposition. And a penalty function is designed to punish singular values without introducing additional parameters. The local information component extracts similar information by an adaptive filter via convolution operation which kernel is obtained by the minimum variance. Finally, we integrate matrix decomposition and local information components via different weights. We apply the proposed method to real-world image datasets and recommendation system datasets. The experimental results demonstrate the proposed model has a lower error and better robustness than several competing matrix completion methods.