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Hyperbolic Knowledge Transfer in Cross-Domain Recommendation System

Xin Yang, Heng Chang, Zhijian Lai, Jinze Yang, Xingrun Li, Yu Lu, Shuaiqiang Wang, Dawei Yin, Erxue Min

TL;DR

The paper tackles data sparsity and long-tail challenges in Cross-Domain Recommendation by introducing Hyperbolic ConTraStive learning (HCTS), which embeds source and target domains on curvature-adaptive hyperbolic manifolds. It combines independent domain GNN embeddings with per-domain hyperbolic projections, and introduces manifold alignment, hyperbolic contrastive learning (across user-user, user-item, and item-item relations), and embedding center calibration to enable robust cross-domain knowledge transfer. The approach achieves consistent improvements over Euclidean baselines and other cross-domain methods, particularly for tail items, validating hyperbolic representations as a powerful tool for modeling hierarchical and long-tail data in CDR. The framework offers a scalable, principled way to leverage auxiliary data from multiple domains while preserving domain-specific structure and improving practical recommendations.

Abstract

Cross-Domain Recommendation (CDR) seeks to utilize knowledge from different domains to alleviate the problem of data sparsity in the target recommendation domain, and it has been gaining more attention in recent years. Although there have been notable advancements in this area, most current methods represent users and items in Euclidean space, which is not ideal for handling long-tail distributed data in recommendation systems. Additionally, adding data from other domains can worsen the long-tail characteristics of the entire dataset, making it harder to train CDR models effectively. Recent studies have shown that hyperbolic methods are particularly suitable for modeling long-tail distributions, which has led us to explore hyperbolic representations for users and items in CDR scenarios. However, due to the distinct characteristics of the different domains, applying hyperbolic representation learning to CDR tasks is quite challenging. In this paper, we introduce a new framework called Hyperbolic Contrastive Learning (HCTS), designed to capture the unique features of each domain while enabling efficient knowledge transfer between domains. We achieve this by embedding users and items from each domain separately and mapping them onto distinct hyperbolic manifolds with adjustable curvatures for prediction. To improve the representations of users and items in the target domain, we develop a hyperbolic contrastive learning module for knowledge transfer. Extensive experiments on real-world datasets demonstrate that hyperbolic manifolds are a promising alternative to Euclidean space for CDR tasks.

Hyperbolic Knowledge Transfer in Cross-Domain Recommendation System

TL;DR

The paper tackles data sparsity and long-tail challenges in Cross-Domain Recommendation by introducing Hyperbolic ConTraStive learning (HCTS), which embeds source and target domains on curvature-adaptive hyperbolic manifolds. It combines independent domain GNN embeddings with per-domain hyperbolic projections, and introduces manifold alignment, hyperbolic contrastive learning (across user-user, user-item, and item-item relations), and embedding center calibration to enable robust cross-domain knowledge transfer. The approach achieves consistent improvements over Euclidean baselines and other cross-domain methods, particularly for tail items, validating hyperbolic representations as a powerful tool for modeling hierarchical and long-tail data in CDR. The framework offers a scalable, principled way to leverage auxiliary data from multiple domains while preserving domain-specific structure and improving practical recommendations.

Abstract

Cross-Domain Recommendation (CDR) seeks to utilize knowledge from different domains to alleviate the problem of data sparsity in the target recommendation domain, and it has been gaining more attention in recent years. Although there have been notable advancements in this area, most current methods represent users and items in Euclidean space, which is not ideal for handling long-tail distributed data in recommendation systems. Additionally, adding data from other domains can worsen the long-tail characteristics of the entire dataset, making it harder to train CDR models effectively. Recent studies have shown that hyperbolic methods are particularly suitable for modeling long-tail distributions, which has led us to explore hyperbolic representations for users and items in CDR scenarios. However, due to the distinct characteristics of the different domains, applying hyperbolic representation learning to CDR tasks is quite challenging. In this paper, we introduce a new framework called Hyperbolic Contrastive Learning (HCTS), designed to capture the unique features of each domain while enabling efficient knowledge transfer between domains. We achieve this by embedding users and items from each domain separately and mapping them onto distinct hyperbolic manifolds with adjustable curvatures for prediction. To improve the representations of users and items in the target domain, we develop a hyperbolic contrastive learning module for knowledge transfer. Extensive experiments on real-world datasets demonstrate that hyperbolic manifolds are a promising alternative to Euclidean space for CDR tasks.
Paper Structure (33 sections, 1 theorem, 36 equations, 11 figures, 5 tables)

This paper contains 33 sections, 1 theorem, 36 equations, 11 figures, 5 tables.

Table of Contents

  1. Introduciton
  2. Preliminaries
  3. Hyperbolic Geometry
  4. Cross-domain Recommendation
  5. Methodology
  6. Framework Overview
  7. Embedding Layer
  8. Single Domain GNN Aggregator
  9. Hyperbolic Manifold Projection
  10. Knowledge Transfer via Hyperbolic Contrastive Learning
  11. Hyperbolic Margin Ranking Loss
  12. Multi-task Optimization
  13. Experiments
  14. Experimental Setup
  15. Datasets and Evaluation Protocols.
  16. ...and 18 more sections

Key Result

Proposition 1

$\langle \cdot, \cdot \rangle_{\mathcal{M}}$ is only a pseudo-inner product on $\mathbb{R}^{n+1}$, however, it is an inner product restricted to the tangent spaces of $\mathcal{H}^{n,K}$, i.e., is a well-defined inner product on $T_x\mathcal{H}^{n,K}$ for all $x \in \mathcal{H}^{n,K}$. Then, $\|u\|_{\mathcal{M}} = \sqrt{\langle u, u \rangle_{\mathcal{M}}}$ is a well-defined norm on it.

Figures (11)

  • Figure 2: The overall framework of HCTS. Graphs from the source and target domains are initially represented through independent embedding layers and skip-GCN layers to generate embeddings. Subsequently, these embeddings are mapped onto two distinct hyperbolic manifolds, each with an adaptive curvature, using an exponential map function for the source and target domains respectively. Predictions are made on these hyperbolic manifolds. To facilitate knowledge transfer from domain $\mathcal{A}$ to domain $\mathcal{B}$, the embeddings from one domain are transposed onto the hyperbolic manifold of the other domain using Equation \ref{['ks-kt']} and three contrastive learning tasks across domains are learned on the unified manifold. Additionally, a calibration task is designed to alleviate the embedding center deviation issue, avoiding the distortion of hyperbolic representations.
  • Figure 4: The deviation of embeddings from the north pole.
  • Figure 5: Visualisation of item embeddings of BiTGCF in the two-dimensional Euclidean space (left), HCTS without embedding center calibration in the Poincaré representation of hyperbolic space (center) and HCTS without embedding center calibration in the Poincaré representation of hyperbolic space (right).
  • Figure 6: Sensitivity analysis on hyperparameters.
  • Figure : (a) Long-tail distribution in Douban Book and Douban Movie datasets.
  • ...and 6 more figures

Theorems & Definitions (2)

  • Proposition 1
  • definition 1