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Big Data Mining and Analytics  2018, Vol. 01 Issue (04): 308-323    DOI: 10.26599/BDMA.2018.9020008
A Survey of Matrix Completion Methods for Recommendation Systems
Andy Ramlatchan, Mengyun Yang, Quan Liu, Min Li, Jianxin Wang, Yaohang Li*
Andy Ramlatchan is with NASA Langley Research Center, Hampton, VA 23666, USA and the Department of Computer Science, Old Dominion University, Norfolk, VA 23666, USA. E-mail:
Mengyun Yang is with the Department of Computer Science, Central South University, Changsha 410083, China and the Department of Science, Shaoyang University, Shaoyang 422000, China. E-mail:
Quan Liu, Min Li, and Jianxin Wang are with the Department of Computer Science, Central South University, Changsha 410083, China. E-mail:;;
Yaohang Li is with the Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA.
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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.

Key wordsmatrix completion      collaborative filtering      recommendation systems     
Received: 21 January 2018      Published: 13 January 2020
Corresponding Authors: Yaohang Li   
Cite this article:

Andy Ramlatchan, Mengyun Yang, Quan Liu, Min Li, Jianxin Wang, Yaohang Li. A Survey of Matrix Completion Methods for Recommendation Systems. Big Data Mining and Analytics, 2018, 01(04): 308-323.

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Fig. 1 Heterogeneous drugs-diseases network.
Fig. 2 Association matrix.
Fig. 3 Game matrix of 364 NCAA division I basketball teams. The <i>x</i>- and <i>y</i>-axes represent the NCAA teams and each point indicates there is a match between the two team during the regular season.
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