Geometric Inductive Matrix Completion: A Hyperbolic Approach with Unified Message Passing

Abstract

Collaborative filtering is a central task in a broad range of recommender systems. As traditional methods train latent variables for user/item individuals under a transductive setting, it requires re-training for out-of-sample inferences. Inductive matrix completion (IMC) solves this problem by learning transformation functions upon engineered features, but it sacrifices model expressiveness and highly depends on feature qualities. In this paper, we propose Geometric Inductive Matrix Completion (GIMC) by introducing hyperbolic geometry and a unified message passing scheme into this generic task. The proposed method is the earliest attempt utilizing capacious hyperbolic space to enhance the capacity of IMC. It is the first work defining continuous explicit feedback prediction within non-Euclidean space by introducing hyperbolic regression for vertex interactions. This is also the first to provide comprehensive evidence that edge semantics can significantly improve recommendations, which is ignored by previous works. The proposed method outperforms the state-of-the-art algorithms with less than 1% parameters compared to its transductive counterparts. Extensive analysis and ablation studies are conducted to reveal the design considerations and practicability for a positive impact to the research community.