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Recommender systems are widely used to recommend the most appealing items tousers. These recommendations can be generated by applying collaborativefiltering methods. The low-rank matrix completion method is thestate-of-the-art collaborative filtering method. In this work, we show that theskewed distribution of ratings in the user-item rating matrix of real-worlddatasets affects the accuracy of matrix-completion-based approaches. Also, weshow that the number of ratings that an item or a user has positivelycorrelates with the ability of low-rank matrix-completion-based approaches topredict the ratings for the item or the user accurately. Furthermore, we usethese insights to develop four matrix completion-based approaches, i.e.,Frequency Adaptive Rating Prediction (FARP), Truncated Matrix Factorization(TMF), Truncated Matrix Factorization with Dropout (TMF + Dropout) and InverseFrequency Weighted Matrix Factorization (IFWMF), that outperforms traditionalmatrix-completion-based approaches for the users and the items with few ratingsin the user-item rating matrix.

Adaptive Matrix Completion for the Users and the Items in Tail