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Hypergraph Contrastive Learning for both Homophilic and Heterophilic Hypergraphs

Renchu Guan, Xuyang Li, Yachao Zhang, Wei Pang, Fausto Giunchiglia, Ximing Li, Yonghao Liu, Xiaoyue Feng

TL;DR

HONOR tackles the challenge of learning representations on hypergraphs with mixed homophily and heterophily by introducing a dual-view, high-pass contrastive framework. It combines a prompt-based view and an adaptive attention-based view to explicitly model heterophilic node–hyperedge relationships, reinforced by degree-based structural augmentation and a high-pass hypergraph encoder. The training objective blends contrastive learning with structural decoupling and covariance regularization, yielding robust, discriminative embeddings validated by theory and extensive experiments. This approach enables effective unsupervised learning on diverse hypergraph structures with potential impact on tasks like node classification and clustering in real-world, high-order relational data.

Abstract

Hypergraphs, as a generalization of traditional graphs, naturally capture high-order relationships. In recent years, hypergraph neural networks (HNNs) have been widely used to capture complex high-order relationships. However, most existing hypergraph neural network methods inherently rely on the homophily assumption, which often does not hold in real-world scenarios that exhibit significant heterophilic structures. To address this limitation, we propose \textbf{HONOR}, a novel unsupervised \textbf{H}ypergraph c\textbf{ON}trastive learning framework suitable for both hom\textbf{O}philic and hete\textbf{R}ophilic hypergraphs. Specifically, HONOR explicitly models the heterophilic relationships between hyperedges and nodes through two complementary mechanisms: a prompt-based hyperedge feature construction strategy that maintains global semantic consistency while suppressing local noise, and an adaptive attention aggregation module that dynamically captures the diverse local contributions of nodes to hyperedges. Combined with high-pass filtering, these designs enable HONOR to fully exploit heterophilic connection patterns, yielding more discriminative and robust node and hyperedge representations. Theoretically, we demonstrate the superior generalization ability and robustness of HONOR. Empirically, extensive experiments further validate that HONOR consistently outperforms state-of-the-art baselines under both homophilic and heterophilic datasets.

Hypergraph Contrastive Learning for both Homophilic and Heterophilic Hypergraphs

TL;DR

HONOR tackles the challenge of learning representations on hypergraphs with mixed homophily and heterophily by introducing a dual-view, high-pass contrastive framework. It combines a prompt-based view and an adaptive attention-based view to explicitly model heterophilic node–hyperedge relationships, reinforced by degree-based structural augmentation and a high-pass hypergraph encoder. The training objective blends contrastive learning with structural decoupling and covariance regularization, yielding robust, discriminative embeddings validated by theory and extensive experiments. This approach enables effective unsupervised learning on diverse hypergraph structures with potential impact on tasks like node classification and clustering in real-world, high-order relational data.

Abstract

Hypergraphs, as a generalization of traditional graphs, naturally capture high-order relationships. In recent years, hypergraph neural networks (HNNs) have been widely used to capture complex high-order relationships. However, most existing hypergraph neural network methods inherently rely on the homophily assumption, which often does not hold in real-world scenarios that exhibit significant heterophilic structures. To address this limitation, we propose \textbf{HONOR}, a novel unsupervised \textbf{H}ypergraph c\textbf{ON}trastive learning framework suitable for both hom\textbf{O}philic and hete\textbf{R}ophilic hypergraphs. Specifically, HONOR explicitly models the heterophilic relationships between hyperedges and nodes through two complementary mechanisms: a prompt-based hyperedge feature construction strategy that maintains global semantic consistency while suppressing local noise, and an adaptive attention aggregation module that dynamically captures the diverse local contributions of nodes to hyperedges. Combined with high-pass filtering, these designs enable HONOR to fully exploit heterophilic connection patterns, yielding more discriminative and robust node and hyperedge representations. Theoretically, we demonstrate the superior generalization ability and robustness of HONOR. Empirically, extensive experiments further validate that HONOR consistently outperforms state-of-the-art baselines under both homophilic and heterophilic datasets.

Paper Structure

This paper contains 17 sections, 3 theorems, 22 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary Study
  4. Method
  5. Hypergraph Augmentation
  6. Prompt-based View Generation.
  7. Adaptive Attention-based View Generation.
  8. Structural Feature Augmentation.
  9. Hypergraph Encoder
  10. Model Training
  11. Contrastive Loss.
  12. Structural Decoupling Loss.
  13. Covariance Regularization.
  14. Theoretical Analysis
  15. Experiments
  16. ...and 2 more sections

Key Result

Theorem 1

For a community $C_k$ ($k = 1, 2$), we denote $\mathbf{{Z}_{C_k}}$ as the submatrix of $\,$$\mathbf{Z}$ consisting of the embeddings of all nodes in $C_k$. The community mean embedding is defined as $\mu_{C_k} = \frac{1}{|C_k|} \sum_{i \in C_k} z_i$. We define the projections of $\,$$\mathbf{Z}$ ont where $\left\|\cdot\right\|_{F}$ is the class separation, i.e., the Frobenius norm, $\Omega(\cdot)$

Figures (3)

  • Figure 1: Statistics of label entropy on real-world datasets.
  • Figure 2: The overall framework of HONOR.
  • Figure 3: Hyperparameter sensitivity for node classification tasks across multiple datasets.

Theorems & Definitions (5)

  • Definition 1: Label Entropy
  • Definition 2: Heterophilic Pairwise Ratio
  • Theorem 1
  • Theorem 2
  • Theorem 3