Equivariant Hypergraph Diffusion Neural Operators

• URL: http://arxiv.org/abs/2207.06680v1
• Date: Thu, 14 Jul 2022 06:17:00 GMT
• Title: Equivariant Hypergraph Diffusion Neural Operators
• Authors: Peihao Wang, Shenghao Yang, Yunyu Liu, Zhangyang Wang, Pan Li
• Abstract summary: Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data. This work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets.
• Score: 81.32770440890303
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%$\uparrow$ in prediction accuracy over four datasets therein.

Related papers

• SPHINX: Structural Prediction using Hypergraph Inference Network [19.853413818941608]
  We introduce Structural Prediction using Hypergraph Inference Network (SPHINX), a model that learns to infer a latent hypergraph structure in an unsupervised way. We show that the recent advancement in k-subset sampling represents a suitable tool for producing discrete hypergraph structures. The resulting model can generate the higher-order structure necessary for any modern hypergraph neural network.
  arXiv  Detail & Related papers  (2024-10-04T07:49:57Z)
• Hypergraph Transformer for Semi-Supervised Classification [50.92027313775934]
  We propose a novel hypergraph learning framework, HyperGraph Transformer (HyperGT) HyperGT uses a Transformer-based neural network architecture to effectively consider global correlations among all nodes and hyperedges. It achieves comprehensive hypergraph representation learning by effectively incorporating global interactions while preserving local connectivity patterns.
  arXiv  Detail & Related papers  (2023-12-18T17:50:52Z)
• From Hypergraph Energy Functions to Hypergraph Neural Networks [94.88564151540459]
  We present an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings. We draw parallels between the proposed bilevel hypergraph optimization, and existing GNN architectures in common use.
  arXiv  Detail & Related papers  (2023-06-16T04:40:59Z)
• Tensorized Hypergraph Neural Networks [69.65385474777031]
  We propose a novel adjacency-tensor-based textbfTensorized textbfHypergraph textbfNeural textbfNetwork (THNN) THNN is faithful hypergraph modeling framework through high-order outer product feature passing message. Results from experiments on two widely used hypergraph datasets for 3-D visual object classification show the model's promising performance.
  arXiv  Detail & Related papers  (2023-06-05T03:26:06Z)
• Relation Embedding based Graph Neural Networks for Handling Heterogeneous Graph [58.99478502486377]
  We propose a simple yet efficient framework to make the homogeneous GNNs have adequate ability to handle heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Networks (RE-GNNs), which employ only one parameter per relation to embed the importance of edge type relations and self-loop connections.
  arXiv  Detail & Related papers  (2022-09-23T05:24:18Z)
• Learnable Hypergraph Laplacian for Hypergraph Learning [34.28748027233654]
  HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. We propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD) HERALD adaptively optimize the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned.
  arXiv  Detail & Related papers  (2021-06-12T02:07:07Z)
• Learnable Hypergraph Laplacian for Hypergraph Learning [34.28748027233654]
  HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. We propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD) HERALD adaptively optimize the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned.
  arXiv  Detail & Related papers  (2021-06-10T12:37:55Z)
• Residual Enhanced Multi-Hypergraph Neural Network [26.42547421121713]
  HyperGraph Neural Network (HGNN) is the de-facto method for hypergraph representation learning. We propose the Residual enhanced Multi-Hypergraph Neural Network, which can fuse multi-modal information from each hypergraph effectively.
  arXiv  Detail & Related papers  (2021-05-02T14:53:32Z)
• HNHN: Hypergraph Networks with Hyperedge Neurons [90.15253035487314]
  HNHN is a hypergraph convolution network with nonlinear activation functions applied to both hypernodes and hyperedges. We demonstrate improved performance of HNHN in both classification accuracy and speed on real world datasets when compared to state of the art methods.
  arXiv  Detail & Related papers  (2020-06-22T14:08:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.