Matrix completion with side information of social network

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. Low-rank matrix completion theories play an essential role in the recommendation system. It is not until recently that auxiliary covariates, such as users’ demographics and products’ attributes, are incorporated into the matrix completion problems. Especially, social network information generates new insights about user behaviors. To fully utilize the social network information, in this thesis, 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 main results demonstrate the 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 our method outperforms the existing approaches, especially when data have small signals. Moreover, our method yields robust estimation with 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.