HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization

Abstract

In large-scale recommender systems, the user-item networks are generally scale-free or expand exponentially. The latent features (also known as embeddings) used to describe the user and item are determined by how well the embedding space fits the data distribution. Hyperbolic space offers a spacious room to learn embeddings with its negative curvature and metric properties, which can well fit data with tree-like structures. Recently, several hyperbolic approaches have been proposed to learn high-quality representations for the users and items. However, most of them concentrate on developing the hyperbolic similitude by designing appropriate projection operations, whereas many advantageous and exciting geometric properties of hyperbolic space have not been explicitly explored. For example, one of the most notable properties of hyperbolic space is that its capacity space increases exponentially with the radius, which indicates the area far away from the hyperbolic origin is much more embeddable. Regarding the geometric properties of hyperbolic space, we bring up a Hyperbolic Regularization powered Collaborative Filtering(HRCF) and design a geometric-aware hyperbolic regularizer. Specifically, the proposal boosts optimization procedure via the root alignment and origin-aware penalty, which is simple yet impressively effective. Through theoretical analysis, we further show that our proposal is able to tackle the over-smoothing problem caused by hyperbolic aggregation and also brings the models a better discriminative ability. We conduct extensive empirical analysis, comparing our proposal against a large set of baselines on several public benchmarks. The empirical results show that our approach achieves highly competitive performance and surpasses both the leading Euclidean and hyperbolic baselines by considerable margins.

Proceedings of the ACM Web Conference 2022 (WWW '22); fixed some typos

References in corpus (6)

• Neural Graph Collaborative Filtering
• Graph Convolutional Neural Networks for Web-Scale Recommender Systems
• Stochastic gradient descent on Riemannian manifolds
• Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking
• Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space
• Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems

Cited by in corpus (9)

• COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learning
• HICF: Hyperbolic Informative Collaborative Filtering
• HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction
• BSAL: A Framework of Bi-component Structure and Attribute Learning for Link Prediction
• Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning
• HGCH: A Hyperbolic Graph Convolution Network Model for Heterogeneous Collaborative Graph Recommendation
• Review-Based Hyperbolic Cross-Domain Recommendation
• DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks
• SPARK: Adaptive Low-Rank Knowledge Graph Modeling in Hybrid Geometric Spaces for Recommendation