HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network

2024-02-15

arXiv.org

AI Summary

Hypergraphs naturally model multi-way relationships, yet existing hypergraph neural networks often reduce them to ordinary graphs via symmetric matrix approximation, discarding higher-order structural and directional information. To address this, we propose a hypergraph neural network grounded in irreversible Markov chains. Our approach introduces the magnetic Laplacian—a complex Hermitian matrix—into hypergraph representation learning for the first time, circumventing symmetric reduction. By leveraging complex-domain graph convolution, it explicitly captures hyperedge directionality and higher-order semantics. Extensive experiments on multiple benchmark datasets for node classification demonstrate that our method consistently outperforms state-of-the-art graph-reduction-based hypergraph models. These results validate the effectiveness and robustness of the magnetic Laplacian in representing higher-order relational structures.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks.

Problem

• Modeling multi-way relations in hypergraphs effectively
• Avoiding information loss from graph-reduction approaches
• Improving node classification with magnetic Laplacian

Innovation

• Non-reversible Markov chain hypergraph representation
• Complex Hermitian magnetic Laplacian matrix
• Outperforms graph-reduction based approaches