Collaborative Filtering With Awareness of Social Networks

Abstract

In this article, we present the NetRec method to leverage the social network data of users in collaborative filtering. We formulate two new network-related terms and obtain convex optimization problems that incorporate assumptions regarding users’ social connections and preferences about products. Our theory demonstrates that this procedure leads to a sharper error bound than before, as long as the observed social network is well structured. We point out that the larger the noise magnitude in the observed user preferences, the larger the reduction in the magnitude of the error bound. Moreover, our theory shows that the combination of the network-related term and the previously used term of nuclear norm gives estimates better than those achieved by any of them alone. We provide an algorithm to solve the new optimization problem and prove that it is guaranteed to find a global optimum. Both simulations and real data experiments are carried out to validate our theoretical findings. The application of the NetRec method on the Yelp data demonstrate its superiority over a state-of-the-art social recommendation method.

Keywords:

• Low-rank
• Matrix completion
• Recommender system
• Social network

Acknowledgments

The authors thank to the associate editor and two anonymous referees for their insightful comments that help improve the article.

Supplementary Material

R code: A zip file containing the code for realizing the NetRec method in R, including an example of applying the NetRec method on the Yelp data.

Proof (Appendix A): Proof for Theorems, Lemmas and Remarks in Section 3 and 4.3.

Additional experiments on the Yelp data (Appendix B): Three additional experiments are reported. They further examine the performance of the proposed method in different aspects.

Simulations about ${\mathrm{P}}_{\text{net}}$ (Appendix C): Numerical evidence for superiority of defining ${\mathrm{P}}_{\text{net}}(X)$ (5) with X_R than with X.

Details about experiments (Appendix D): Details about experiments in Sections 5.1.3 and 5.2.

Additional information

Funding

Jing’s research is partially supported by the HK RGC Grants GRF16302020, GRF 16304419, GRF 16305616, and The State Key Program of National Natural Science Foundation of China grant NSFC11631003.