Abstract: Robust product recommendation enables internet platforms to boost their business. However, in practice, the user-product rating matrix often has many missing entries. Social network information generates new insights about user behaviors. To fully use such information, we develop a novel approach, called MCNet, that combines the random dot product graph model and low-rank matrix completion to recover missing entries in a user-product rating matrix. 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 existing approaches, especially when the data have small signals. Moreover, MCNet yields robust estimation under misspecified models. We apply MCNet and its competitors to predict the missing entries in the user-product rating matrices of the Yelp and Douban movie platforms. The results show that, in general, MCNet gives the smallest testing errors among the comparative methods.

Key words and phrases: Low-rank estimation, matrix completion, missing data, random dot product graph, social network.