Robust collaborative filtering based on non-negative matrix factorization and R1-norm

Collaborative filtering systems are vulnerable to shilling attacks or profile injection attacks in which malicious users can deliberately manipulate the systems' recommendation output by inserting a number of fake profiles. To address this issue, some robust collaborative filtering methods based on matrix factorization have been proposed. However, these methods suffer from low robustness and recommendation accuracy because they use the squared error function as the loss function that can be easily dominated by large residuals. In this paper we propose a robust collaborative filtering method based on non-negative matrix factorization and R1-norm. Firstly, we introduce R1-norm to construct a robust non-negative matrix factorization model for collaborative filtering and make an analysis of the stability of the model. Secondly, we propose an iterative optimization method of feature matrices based on the iterative updating algorithm of non-negative matrix factorization, which guarantees that the predicted ratings are accurate and non-negative. Finally, we devise a robust collaborative filtering algorithm based on the proposed model. Experimental results on two different datasets show that the proposed method can improve the robustness and recommendation accuracy.