A differentially private nonnegative matrix factorization for recommender system

Abstract

Nonnegative matrix factorization (NMF)-based models have been proven to be highly effective and scalable in addressing collaborative filtering (CF) problems in the recommender system (RS). Since RS requires tremendous user data to provide personalized information services, the issue of data privacy has gained prominence. Although the differential privacy (DP) technique has been widely applied to RS, the requirement of nonnegativity makes it difficult to successfully incorporate DP into NMF. In this paper, a differentially private NMF (DPNMF) method is proposed by perturbing the coefficients of the polynomial expression of the objective function, which achieves a good trade-off between privacy protection and recommendation quality. Moreover, to alleviate the influence of the noises added by DP on the items with sparse ratings, an imputation-based DPNMF (IDPNMF) method is proposed. Theoretic analyses and experimental results on several benchmark datasets show that the proposed schemes have good performance and can achieve better recommendation quality on large-scale datasets. Therefore, our schemes have high potential to implement privacy-preserving RS based on big data.