A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising

TL;DR

This paper establishes a theoretical connection between hypergraph signal denoising and tensor hypergraph neural networks, leading to a novel iterative network design with promising experimental results.

Contribution

It reveals an equivalence between HyperGSD and T-HGCN, and introduces T-HGIN, a new iterative hypergraph neural network based on HyperGSD principles.

Findings

T-HGIN outperforms existing methods in denoising tasks

Theoretical link between HyperGSD and T-HGCN is established

Numerical experiments demonstrate the effectiveness of T-HGIN

Abstract

Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel HyperGNNs from a HyperGSD perspective, and vice versa. In particular, the tensor-hypergraph convolutional network (T-HGCN) has emerged as a powerful architecture for preserving higher-order interactions on hypergraphs, and this work shows an equivalence relation between a HyperGSD problem and the T-HGCN. Inspired by this intriguing result, we further design a tensor-hypergraph iterative network (T-HGIN) based on the HyperGSD problem, which takes advantage of a multi-step updating scheme in every single layer. Numerical experiments are conducted to show the promising applications of the proposed T-HGIN approach.