Collaborative Filtering With Awareness of Social Networks

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. © 2021 American Statistical Association.