A Unified View Between Tensor Hypergraph Neural Networks And Signal
  Denoising
Fuli Wang Karelia Pena-Pena Wei Qian Gonzalo R. Arce
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.