Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets
2026-06-08 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore a new way to apply the U-Net architecture, commonly used in image tasks, to hypergraph data, which is a more complex network structure. They solve a tough problem of how to simplify (pool) and then rebuild (unpool) hypergraphs without losing important details, using a method inspired by hierarchical clustering. Their approach processes these steps globally and in parallel, unlike previous methods that worked step-by-step and could damage the structure. They tested their method on tasks like hypergraph reconstruction, classification, and spotting anomalies, showing better results than current leading techniques.
ConvolutionHypergraphU-NetPoolingUnpoolingHierarchical ClusteringDendrogramGraph Deep LearningAnomaly DetectionGraph Classification
Authors
Fuli Wang, Wei Qian, Daniel L. Lau, Gonzalo R. Arce
Abstract
Convolutions have successfully transitioned from image processing to the complex realm of non-Euclidean higher-order domains, particularly in hypergraphs. Despite the success in convolution, the exploration of a popular architecture named U-Net remains largely unexplored for hypergraph data due to the lack of well-defined pooling and unpooling operations. This work pioneers the study of U-Net architectures for hypergraph data, addressing the critical challenge of designing effective pooling and unpooling operations that retain maximal structural information from the input hypergraph. Motivated by hierarchical clustering, we propose to construct the pooling and unpooling operators all at once by cutting the clustering dendrogram at different granularities, named the Parallel Hierarchical Pooling (PHPool) and Unpooling (PHUnpool) operators. Unlike existing pooling methods that risk local structural damage through a sequential learning procedure, our PHPool operators are designed in a global and parallel manner to ensure fidelity to the original hypergraph structure with efficient computation while the PHUnpool operators are tailored to perform inverse operations of the PHPools for hypergraph reconstruction. We validate our model through hypergraph reconstruction simulation, hypergraph classification, and node-level anomaly detection, where it demonstrates superior performance over existing state-of-the-art graph and hypergraph deep learning methods.