Robust Recommendation via Social Network Enhanced Matrix Completion

Abstract

Robust product recommendation is crucial for internet platforms to boost their businesses. One challenge though is that the user-product rating matrix often has many missing entries. Social network information generates new insights about user behaviors. To fully utilize the social network information, we develop a novel approach, namely MCNet, which combines the random dot product graph model and the low-rank matrix completion to recover the missing entries in the user-product rating matrix from the internet platform. Our algorithm improves the accuracy and the efficiency of recovering the incomplete matrices. We study the asymptotic properties of the estimator. Furthermore, we perform extensive simulations and show that MCNet outperforms the existing approaches, especially when data have small signals. Moreover, MCNet yields robust estimation under misspecified models. We apply MCNet and the competitors to predict the missing entries in the user-product rating matrices on the Yelp and Douban movie platforms. MCNet generally gives the smallest testing errors among all the comparative methods.