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A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide

Sunwoo Kim, Soo Yong Lee, Yue Gao, Alessia Antelmi, Mirko Polato, Kijung Shin

TL;DR

This survey addresses the rise of hypergraph neural networks (HNNs) for learning from higher-order interactions by providing a structured, step-by-step guide. It develops a three-part encoder design framework (features, hypergraph representations, and message passing) and three training objectives (classification, contrastive learning, generation), detailing how each component handles HOIs. The paper also guides practitioners across major domains—recommendation, bioinformatics/medicine, time series, and computer vision—on hypergraph construction and task formulation, complemented by discussions of limitations and future directions. Overall, it clarifies how to design, train, and apply HNNs to effectively exploit higher-order structure in real-world data.

Abstract

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, bioinformatics and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.

A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide

TL;DR

This survey addresses the rise of hypergraph neural networks (HNNs) for learning from higher-order interactions by providing a structured, step-by-step guide. It develops a three-part encoder design framework (features, hypergraph representations, and message passing) and three training objectives (classification, contrastive learning, generation), detailing how each component handles HOIs. The paper also guides practitioners across major domains—recommendation, bioinformatics/medicine, time series, and computer vision—on hypergraph construction and task formulation, complemented by discussions of limitations and future directions. Overall, it clarifies how to design, train, and apply HNNs to effectively exploit higher-order structure in real-world data.

Abstract

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, bioinformatics and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.
Paper Structure (44 sections, 15 equations, 3 figures, 2 tables)

This paper contains 44 sections, 15 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Encoder Design Guidance
  4. Step 1: Design features to reflect HOIs
  5. External features or labels
  6. Structural features
  7. Identity features
  8. Comparison with GNNs
  9. Step 2: Express hypergraphs to reflect HOIs
  10. Reductive transformation
  11. Non-reductive transformation
  12. Comparison with GNNs
  13. Step 3: Pass messages to reflect HOIs
  14. Whose messages to aggregate (target selection)
  15. What messages to aggregate (message representation)
  16. ...and 29 more sections

Figures (3)

  • Figure 1: An example hypergraph modeling the co-authorship relationship among five authors across three publications. Each node represents an author, while each hyperedge includes all co-authors of a publication.
  • Figure 2: Taxonomy on modeling higher-order interactions. The term neg. sam. denotes negative sampling.
  • Figure 3: An example hypergraph (a), its clique-expanded graph (b), and its star-expanded graph (c).