[Paper Review] Hyperbolic Recommender Systems.

Tran Dang Quang Vinh, Yi Tay+3 more|arXiv (Cornell University)|Sep 5, 2018

Recommender Systems and Techniques23 references21 citations

TL;DR

This paper proposes HyperBPR, a hyperbolic recommender system that learns user and item embeddings in hyperbolic space to better capture hierarchical user-item relationships. By leveraging the intrinsic curvature of hyperbolic space, HyperBPR outperforms Euclidean-based models and achieves state-of-the-art performance on benchmark datasets, demonstrating superior representation learning for personalized recommendation.

ABSTRACT

Many well-established recommender systems are based on representation learning in Euclidean space. In these models, matching functions such as the Euclidean distance or inner product are typically used for computing similarity scores between user and item embeddings. This paper investigates the notion of learning user and item representations in Hyperbolic space. In this paper, we argue that Hyperbolic space is more suitable for learning user-item embeddings in the recommendation domain. Unlike Euclidean spaces, Hyperbolic spaces are intrinsically equipped to handle hierarchical structure, encouraged by its property of exponentially increasing distances away from origin. We propose HyperBPR (Hyperbolic Bayesian Personalized Ranking), a conceptually simple but highly effective model for the task at hand. Our proposed HyperBPR not only outperforms their Euclidean counterparts, but also achieves state-of-the-art performance on multiple benchmark datasets, demonstrating the effectiveness of personalized recommendation in Hyperbolic space.

Motivation & Objective

• To investigate whether hyperbolic space is more suitable than Euclidean space for learning user and item embeddings in recommendation systems.
• To address the limitation of Euclidean spaces in modeling hierarchical data structures common in user-item interactions.
• To develop a conceptually simple yet effective model that leverages hyperbolic geometry for personalized ranking.
• To demonstrate that hyperbolic representations can achieve state-of-the-art performance on standard recommendation benchmarks.

Proposed method

• The model learns user and item embeddings in hyperbolic space using the Poincaré ball model, which supports efficient optimization and hierarchical representation.
• It employs a Bayesian Personalized Ranking (BPR) loss function adapted to hyperbolic geometry to optimize ranking preferences.
• The model uses hyperbolic distance as a similarity measure between user and item embeddings, exploiting the exponential growth of space away from the origin.
• Optimization is performed via stochastic gradient descent on the Poincaré ball manifold, preserving the intrinsic geometry of the space.
• The architecture maintains a simple feed-forward design without complex operations, enabling efficient training and inference.
• The method is end-to-end differentiable, allowing backpropagation through the hyperbolic embedding space.

Experimental results

Research questions

• RQ1 Can hyperbolic space better represent hierarchical user-item interaction patterns than Euclidean space in recommendation systems?
• RQ2 How does the curvature of hyperbolic space affect the performance of personalized ranking models?
• RQ3 Does learning in hyperbolic space lead to improved recommendation accuracy compared to state-of-the-art Euclidean models?
• RQ4 To what extent do hyperbolic embeddings capture long-tail and hierarchical item structures in real-world datasets?

Key findings

• HyperBPR achieves state-of-the-art performance on multiple benchmark datasets, outperforming existing Euclidean-based models.
• The model demonstrates superior performance on long-tail items, indicating better capture of hierarchical item structures.
• Hyperbolic representations show improved ranking quality, as measured by metrics such as NDCG and Recall, due to the exponential capacity of hyperbolic space.
• The use of hyperbolic geometry leads to more compact and meaningful representations, especially for sparse user-item interactions.
• The model's performance gain is most pronounced in datasets with strong hierarchical structures, validating the theoretical advantages of hyperbolic space.
• The results confirm that hyperbolic space is intrinsically better suited for modeling hierarchical relationships in recommendation systems.