A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising
This work provides a unified view for researchers in hypergraph modeling, potentially enabling novel network designs, but it appears incremental as it builds on existing tensor-hypergraph architectures.
The paper tackled the problem of connecting hypergraph neural networks and hypergraph signal denoising, showing an equivalence between a denoising problem and a tensor-hypergraph convolutional network, and designed a new tensor-hypergraph iterative network that demonstrated promising results in numerical experiments.
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.