Low-Rank Matrix Completion over Finite Abelian Group Algebras for Context-Aware Recommendation

The incorporation of contextual information is an important part of context-aware recommendation. Many context-aware recommendation systems adopt tensor completion to include contextual information. However, the symmetries between dimensions of a tensor induce an unreasonable assumption that users, items and contexts should be treated equally in recommender systems. In this paper, we address this by using matrices over finite abelian group algebra (AGA) to model context-aware interactions between users and items. Specifically, we formulate context-aware recommendation as a low-rank matrix completion problem over AGA (MC-AGA) and derive a new algorithm using the inexact augmented Lagrange multiplier method. We then test MC-AGA on two real-world datasets: one containing implicit feedback and one with explicit feedback. Experiment results show that MC-AGA outperforms not only existing tensor completion algorithms but also recommendation systems with other context-aware representations.