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

In recent years, hypergraph neural networks have achieved remarkable success in tasks such as node classification, link prediction, and graph classification, thanks to their powerful computational capabilities. However, most existing hypergraph neural networks are restricted to singlelayer hypergraph, making it challenging to effectively capture the intricate intra-layer higher-order relationships and inter-layer interactions in multilayer hypergraph. Furthermore, these methods typically embed hypergraph features in Euclidean space, which often results in significant distortions when dealing with hypernetworks exhibiting scale-free properties or hierarchical structures. Recently, hyperbolic geometric representation learning has emerged as an effective approach to alleviate such embedding distortions. Building on this foundation, we propose a novel Hyperbolic Multi-channel HyperGraph convolutional Neural Network (HMHGNN). Specifically, a multilayer hypergraph model is first constructed based on singlelayer hypergraphs. Then, a multi-channel convolution mechanism is introduced, which integrates hypergraph's derivative graph, hypergraph's line graph, and hyperbolic hypergraph convolution. Subsequently, Euclidean features are mapped to hyperbolic space, and feature transformations are performed within the hyperbolic space. To evaluate the performance of the proposed model, extensive experiments were conducted on three datasets: a scientific collaboration multilayer hypernetwork, a citation multilayer hypernetwork, and a biological multilayer hypernetwork. The experimental results demonstrate that HMHGNN significantly outperforms traditional hypergraph and hyperbolic neural network models in node classification and link prediction tasks. These findings underscore the superior generalization capability and robustness of our model, offering valuable insights into the modeling and analysis of multilayer hypergraph.