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Collaborative filtering is an important topic in data mining and has been widely used in recommendation system. In this paper, we proposed a unified model for collaborative filtering based on graph regularized weighted nonnegative matrix factorization. In our model, two graphs are constructed on users and items, which exploit the internal information (e.g. neighborhood information in the user-item rating matrix) and external information (e.g. content information such as user’s occupation and item’s genre, or other kind of knowledge such as social trust network). The proposed method not only inherits the advantages of model-based method, but also owns the merits of memory-based method which considers the neighborhood information. Moreover, it has the ability to make use of content information and any additional information regarding user-user such as social trust network. Due to the use of these internal and external information, the proposed method is able to find more interpretable lowdimensional representations for users and items, which is helpful for improving the recommendation accuracy. Experimental results on benchmark collaborative filtering data sets demonstrate that the proposed methods outperform the state of the art collaborative filtering methods a lot.

Collaborative Filtering: Weighted Nonnegative Matrix Factorization Incorporating User and Item Graphs