Robust matrix completion for rating-scale data

Abstract

In recent years, there has been significant interest in low-rank matrix completion (LRMC). LRMC aims to predict the unknown entries of a partially observed matrix using its known elements and a low-rank rank constraint while minimizing a specific criterion such as the mean squared error. Although common applications feature discrete rating-scale data, such as the well-known Netflix Prize competition on recommender systems, methods for LRMC are almost always designed for and studied in the context of continuous data matrices. Little is therefore known on the statistical properties of LRMC methods on discrete rating-scale data. Furthermore, while ample work on LRMC exists, only a relatively small subset of the literature has considered matrix completion in the presence of corrupted observations. Yet corrupted observations may widely occur in user-product rating matrices, for instance via malicious users who deliberately manipulate ratings in so-called attacks in order to influence a recommender system to their advantage.
To fill these gaps, we introduce a new LRMC algorithm designed specifically for discrete rating-scale data and robust to the presence of corrupted observations. Furthermore, we evaluate the performance of our proposed method and several competing approaches through simulation studies using discrete rating-scale data instead of continuous data, considering various attack scenarios.