A review on matrix completion for recommender systems

Recommender systems that predict the preference of users have attracted more and more attention in decades. One of the most popular methods in this field is collaborative filtering, which employs explicit or implicit feedback to model the user–item connections. Most methods of collaborative filtering are based on matrix completion techniques which recover the missing values of user–item interaction matrices. The low-rank assumption is a critical premise for matrix completion in recommender systems, which speculates that most information in interaction matrices is redundant. Based on this assumption, a large number of methods have been developed, including matrix factorization models, rank optimization models, and frameworks based on neural networks. In this paper, we first provide a brief description of recommender systems based on matrix completion. Next, several classical and state-of-the-art algorithms related to matrix completion for collaborative filtering are introduced, most of which are based on the assumption of low-rank property. Moreover, the performance of these algorithms is evaluated and discussed by conducting substantial experiments on different real-world datasets. Finally, we provide open research issues for future exploration of matrix completion on recommender systems.