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This paper investigates the notion of learning user and item representationsin non-Euclidean space. Specifically, we study the connection between metriclearning in hyperbolic space and collaborative filtering by exploring Mobiusgyrovector spaces where the formalism of the spaces could be utilized togeneralize the most common Euclidean vector operations. Overall, this work aimsto bridge the gap between Euclidean and hyperbolic geometry in recommendersystems through metric learning approach. We propose HyperML (Hyperbolic MetricLearning), a conceptually simple but highly effective model for boosting theperformance. Via a series of extensive experiments, we show that our proposedHyperML not only outperforms their Euclidean counterparts, but also achievesstate-of-the-art performance on multiple benchmark datasets, demonstrating theeffectiveness of personalized recommendation in hyperbolic geometry.

HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems