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In recent years, the recommendation systems have become increasingly popular and have been used in a broad variety of applications. Here, we investigate the matrix completion techniques for the recommendation systems that are based on collaborative filtering. The collaborative filtering problem can be viewed as predicting the favorability of a user with respect to new items of commodities. When a rating matrix is constructed with users as rows, items as columns, and entries as ratings, the collaborative filtering problem can then be modeled as a matrix completion problem by filling out the unknown elements in the rating matrix. This article presents a comprehensive survey of the matrix completion methods used in recommendation systems. We focus on the mathematical models for matrix completion and the corresponding computational algorithms as well as their characteristics and potential issues. Several applications other than the traditional user-item association prediction are also discussed.


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A Survey of Matrix Completion Methods for Recommendation Systems

Show Author's information Andy RamlatchanMengyun YangQuan LiuMin LiJianxin WangYaohang Li( )
NASA Langley Research Center, Hampton, VA 23666, USA and the Department of Computer Science, Old Dominion University, Norfolk, VA 23666, USA.
Department of Computer Science, Central South University, Changsha 410083, China and the Department of Science, Shaoyang University, Shaoyang 422000, China.
Department of Computer Science, Central South University, Changsha 410083, China.
Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA.

Abstract

In recent years, the recommendation systems have become increasingly popular and have been used in a broad variety of applications. Here, we investigate the matrix completion techniques for the recommendation systems that are based on collaborative filtering. The collaborative filtering problem can be viewed as predicting the favorability of a user with respect to new items of commodities. When a rating matrix is constructed with users as rows, items as columns, and entries as ratings, the collaborative filtering problem can then be modeled as a matrix completion problem by filling out the unknown elements in the rating matrix. This article presents a comprehensive survey of the matrix completion methods used in recommendation systems. We focus on the mathematical models for matrix completion and the corresponding computational algorithms as well as their characteristics and potential issues. Several applications other than the traditional user-item association prediction are also discussed.

Keywords: collaborative filtering, matrix completion, recommendation systems

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Received: 21 January 2018
Accepted: 20 March 2018
Published: 02 July 2018
Issue date: December 2018

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© The author(s) 2018

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This work was supported in part by the National Natural Science Foundation of China (Nos. 61728211 and 1066471).

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