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HGCH: A Hyperbolic Graph Convolution Network Model for Heterogeneous Collaborative Graph Recommendation

Lu Zhang, Ning Wu

TL;DR

HGCH tackles the challenge of leveraging hyperbolic space for heterogeneous collaborative graphs by introducing power-law prior initialization, gyromidpoint-based hyperbolic neighbor aggregation, gate fusion with prior for multi-source fusion, and hyperbolic user-specific negative sampling to speed training. The model operates on a heterogeneous collaborative graph that integrates side information with user-item interactions, enabling richer representations in hyperbolic space. Empirical results on four real datasets show HGCH and its side-information variant HGCH+ outperform state-of-the-art baselines, with faster convergence and particularly strong improvements on tail items, as confirmed by ablations and visualizations. This work advances scalable, effective hyperbolic recommendations in heterogeneous graphs, with practical implications for personalized and diverse recommendations in real systems.

Abstract

User-item interaction data in collaborative filtering and graph modeling tasks often exhibit power-law characteristics, which suggest the suitability of hyperbolic space modeling. Hyperbolic Graph Convolution Neural Networks (HGCNs) are a novel technique that leverages the advantages of GCN and hyperbolic space, and then achieves remarkable results. However, existing HGCN methods have several drawbacks: they fail to fully leverage hyperbolic space properties due to arbitrary embedding initialization and imprecise tangent space aggregation; they overlook auxiliary information that could enrich the collaborative graph; and their training convergence is slow due to margin ranking loss and random negative sampling. To overcome these challenges, we propose Hyperbolic Graph Collaborative for Heterogeneous Recommendation (HGCH), an enhanced HGCN-based model for collaborative filtering that integrates diverse side information into a heterogeneous collaborative graph and improves training convergence speed. HGCH first preserves the long-tailed nature of the graph by initializing node embeddings with power law prior; then it aggregates neighbors in hyperbolic space using the gyromidpoint method for accurate computation; finally, it fuses multiple embeddings from different hyperbolic spaces by the gate fusion with prior. Moreover, HGCH employs a hyperbolic user-specific negative sampling to speed up convergence. We evaluate HGCH on four real datasets, and the results show that HGCH achieves competitive results and outperforms leading baselines, including HGCNs. Extensive ablation studies further confirm its effectiveness.

HGCH: A Hyperbolic Graph Convolution Network Model for Heterogeneous Collaborative Graph Recommendation

TL;DR

HGCH tackles the challenge of leveraging hyperbolic space for heterogeneous collaborative graphs by introducing power-law prior initialization, gyromidpoint-based hyperbolic neighbor aggregation, gate fusion with prior for multi-source fusion, and hyperbolic user-specific negative sampling to speed training. The model operates on a heterogeneous collaborative graph that integrates side information with user-item interactions, enabling richer representations in hyperbolic space. Empirical results on four real datasets show HGCH and its side-information variant HGCH+ outperform state-of-the-art baselines, with faster convergence and particularly strong improvements on tail items, as confirmed by ablations and visualizations. This work advances scalable, effective hyperbolic recommendations in heterogeneous graphs, with practical implications for personalized and diverse recommendations in real systems.

Abstract

User-item interaction data in collaborative filtering and graph modeling tasks often exhibit power-law characteristics, which suggest the suitability of hyperbolic space modeling. Hyperbolic Graph Convolution Neural Networks (HGCNs) are a novel technique that leverages the advantages of GCN and hyperbolic space, and then achieves remarkable results. However, existing HGCN methods have several drawbacks: they fail to fully leverage hyperbolic space properties due to arbitrary embedding initialization and imprecise tangent space aggregation; they overlook auxiliary information that could enrich the collaborative graph; and their training convergence is slow due to margin ranking loss and random negative sampling. To overcome these challenges, we propose Hyperbolic Graph Collaborative for Heterogeneous Recommendation (HGCH), an enhanced HGCN-based model for collaborative filtering that integrates diverse side information into a heterogeneous collaborative graph and improves training convergence speed. HGCH first preserves the long-tailed nature of the graph by initializing node embeddings with power law prior; then it aggregates neighbors in hyperbolic space using the gyromidpoint method for accurate computation; finally, it fuses multiple embeddings from different hyperbolic spaces by the gate fusion with prior. Moreover, HGCH employs a hyperbolic user-specific negative sampling to speed up convergence. We evaluate HGCH on four real datasets, and the results show that HGCH achieves competitive results and outperforms leading baselines, including HGCNs. Extensive ablation studies further confirm its effectiveness.
Paper Structure (38 sections, 20 equations, 5 figures, 5 tables, 1 algorithm)

This paper contains 38 sections, 20 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Convolution Neural Networks
  4. Hyperbolic Recommender Systems
  5. Preliminaries
  6. Hyperbolic Space
  7. Task Formulation
  8. User-Item Bipartite Graphs
  9. Heterogeneous Collaborative Graph
  10. Problem Statement
  11. Method
  12. Embedding Layer with Power Law Prior
  13. Hyperbolic Aggregation and Fusion Layers
  14. Hyperbolic Neighbor Aggregation
  15. Multi-Space Information Fusion
  16. ...and 23 more sections

Figures (5)

  • Figure 1: NDCG@10 changes with training epochs on validation set of Amazon-Book and Yelp2022. Other metric@$K$s show a similar tendency. HGCH converges very fast so only 40 and 60 epochs were trained on Amazon-Book and Yelp2022, respectively.
  • Figure 2: An Example of a Heterogeneous Collaborative Graph. Its node set contains the user, item, and category; its edge set contains the user-item link, user-user link, item-item link and item-category link.
  • Figure 3: An illustration of HGCH model architecture. It consists of three main components: 1) power law prior-based embedding layer, 2) hyperbolic aggregation and fusion layer, and 3) prediction layer. Note that "int" and "aff" denote the subspace "interaction" and "affiliation", respectively. "GP" means gate fusion with prior.
  • Figure 4: Comparison between different fusion methods. B, G, P, and GP represent Base, Gate, Prior, and Gate&Prior, respectively, where the Base is the HGCH.
  • Figure 5: HGCH item embedding visualization in the Poincaré representation of tangent space before and after the graph convolutional layers on the dataset Amazon-Book. Items are categorized into quartiles by popularity, where [75, 100] represents the most popular items. The meaning of Base, PI, HA, and GP are the same as in Section \ref{['sec:aa']}.