Hyperbolic multi-channel hypergraph convolutional neural network based on multilayer hypergraph.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Theory

Background:

• Existing hypergraph neural networks struggle with multilayer structures and Euclidean embedding distortions.
• Hyperbolic geometric representation learning offers a solution for embedding complex network data.
• Multilayer hypergraphs possess intricate intra-layer relationships and inter-layer interactions.

Purpose of the Study:

• To propose a novel Hyperbolic Multi-channel HyperGraph convolutional Neural Network (HMHGNN) for enhanced multilayer hypergraph analysis.
• To overcome the limitations of single-layer hypergraph models and Euclidean embedding distortions.
• To improve performance in node classification and link prediction tasks on complex hypergraph data.

Main Methods:

• Constructing a multilayer hypergraph model from single-layer hypergraphs.
• Implementing a multi-channel convolution mechanism integrating derivative graph, line graph, and hyperbolic convolution.
• Mapping Euclidean features to hyperbolic space for feature transformation.

Main Results:

• HMHGNN significantly outperforms traditional hypergraph and hyperbolic neural network models.
• The model shows superior performance in node classification and link prediction tasks.
• Experiments conducted on scientific collaboration, citation, and biological multilayer hypernetworks validate the model's effectiveness.

Conclusions:

• The proposed HMHGNN model effectively captures higher-order relationships and inter-layer interactions in multilayer hypergraphs.
• Hyperbolic embedding significantly reduces distortions for scale-free or hierarchical hypernetworks.
• HMHGNN exhibits superior generalization capability and robustness, offering valuable insights for multilayer hypergraph analysis.