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. Further analysis verifies the rationality and effectiveness of the proposal for robust, deeper, and lightweight neural graph collaborative filtering.

TeleGraph: A Benchmark Dataset for Hierarchical Link Prediction

“…We further present some characteristics on the topology of Tele-Graph and the statistics are summarized in Table 4, where density [23] and hyperbolicity [4] measure the sparsity and "treelikeness" of a given network, respectively. Specifically, the density is 0 for a graph without edges and 1 for a complete graph, and the hyperbolicity value of approximately zero means a high tree-likeness.…”

Learning Binarized Graph Representations with Multi-faceted Quantization Reinforcement for Top-K Recommendation

“…Full-precision recommender models. (1) Collaborative Filtering (CF) is a prevalent methodology in modern recommender systems [11,64,65]. Earlier CF methods, e.g., Matrix Factorization [32,46], reconstruct historical interactions to learn user-item embeddings.…”

HICF: Hyperbolic Informative Collaborative Filtering

“…gained increasing interest in the recommendation area as the capacity of hyperbolic space exponentially increases with radius, which fits nicely with a power-law distributed user-item network. Naturally, models based on hyperbolic graph neural networks achieve competitive performance in recommender systems [4,33,43]. However, it is not clear in what respects the hyperbolic model is superior to the Euclidean counterpart.…”