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Recommender systems collect various kinds of data to create their recommendations. Collaborative filtering is a common technique in this area. This technique gathers and analyzes information on users preferences, and then estimates what users will like based on their similarity to other users. However, most of current collaborative filtering approaches have faced two problems: sparsity and scalability. This paper proposes a novel method by applying non-negative matrix factorization, which alleviates these problems via matrix factorization and similarity. Non-negative matrix factorization attempts to find two non-negative matrices whose product can well approximate the original matrix. It also imposes non-negative constraints on the latent factors. The proposed method presents novel update rules to learn the latent factors for predicting unknown rating. Unlike most of collaborative filtering methods, the proposed method can predict all the unknown ratings. It is easily implemented and its computational complexity is very low. Empirical studies on MovieLens and Book-Crossing datasets display that the proposed method is more tolerant against the problems of sparsity and scalability, and obtains good results.

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