Abstract
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.
Highlights
Matrix completion is to restore the missing entries in a sparse matrix based on partial observation entries, and has been enjoyed widespread applications in recent years, such as recommendation systems [1], [2], image processing [3]–[5], social networks [6], [7], large scale classification [8] and clustering [9]
The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) of the proposed LAMC algorithm are smaller than other methods in general, especially for MovieLens 1M and Book-Crossing datasets
To further verify the completion preference of our method, we show the RMSE versus time obtained from the low-rank matrix factorization
Summary
Matrix completion is to restore the missing entries in a sparse matrix based on partial observation entries, and has been enjoyed widespread applications in recent years, such as recommendation systems [1], [2], image processing [3]–[5], social networks [6], [7], large scale classification [8] and clustering [9]. In these applications, authors obtain the completed matrix by assuming the observed matrix has a lowrank or approximately low-rank structure.
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