Community and hyperedge inference in multiple hypergraphs

• URL: http://arxiv.org/abs/2505.04967v1
• Date: Thu, 08 May 2025 05:52:41 GMT
• Title: Community and hyperedge inference in multiple hypergraphs
• Authors: Li Ni, Ziqi Deng, Lin Mu, Lei Zhang, Wenjian Luo, Yiwen Zhang,
• Abstract summary: We show how to utilize interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems.<n>We propose a model based on the block model, which integrates information from multiple hypergraphs to reveal latent high-order structures.<n>Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.
• Score: 9.782518418521175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding relationship between genes and their protein products, drive the establishment of interconnections between multiple hypergraphs. Here, we demonstrate how to utilize those interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems, thereby enhancing understanding of underlying structures. We propose a model based on the stochastic block model, which integrates information from multiple hypergraphs to reveal latent high-order structures. Real-world hyperedges exhibit preferential attachment, where certain nodes dominate hyperedge formation. To characterize this phenomenon, our model introduces hyperedge internal degree to quantify nodes' contributions to hyperedge formation. This model is capable of mining communities, predicting missing hyperedges of arbitrary sizes within hypergraphs, and inferring inter-hypergraph edges between hypergraphs. We apply our model to high-order datasets to evaluate its performance. Experimental results demonstrate strong performance of our model in community detection, hyperedge prediction, and inter-hypergraph edge prediction tasks. Moreover, we show that our model enables analysis of multiple hypergraphs of different types and supports the analysis of a single hypergraph in the absence of inter-hypergraph edges. Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.

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)
• Sheaf Hypergraph Networks [10.785525697855498]
  We introduce cellular sheaves for hypergraphs, a mathematical construction that adds extra structure to the conventional hypergraph. Drawing inspiration from existing Laplacians in the literature, we develop two unique formulations of sheaf hypergraph Laplacians. We employ these sheaf hypergraph Laplacians to design two categories of models: Sheaf Hypergraph Neural Networks and Sheaf Hypergraph Convolutional Networks.
  arXiv  Detail & Related papers  (2023-09-29T10:25:43Z)
• 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)
• Augmentations in Hypergraph Contrastive Learning: Fabricated and Generative [126.0985540285981]
  We apply the contrastive learning approach from images/graphs (we refer to it as HyperGCL) to improve generalizability of hypergraph neural networks. We fabricate two schemes to augment hyperedges with higher-order relations encoded, and adopt three augmentation strategies from graph-structured data. We propose a hypergraph generative model to generate augmented views, and then an end-to-end differentiable pipeline to jointly learn hypergraph augmentations and model parameters.
  arXiv  Detail & Related papers  (2022-10-07T20:12:20Z)
• Equivariant Hypergraph Diffusion Neural Operators [81.32770440890303]
  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.
  arXiv  Detail & Related papers  (2022-07-14T06:17:00Z)
• Principled inference of hyperedges and overlapping communities in hypergraphs [0.0]
  We propose a framework based on statistical inference to characterize the structural organization of hypergraphs. We show strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges.
  arXiv  Detail & Related papers  (2022-04-12T09:13:46Z)
• Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs [59.71134113268709]
  We present General Hypergraph Spectral Convolution(GHSC), a general learning framework that can handle EDVW and EIVW hypergraphs. In this paper, we show that the proposed framework can achieve state-of-the-art performance. Experiments from various domains including social network analysis, visual objective classification, protein learning demonstrate that the proposed framework can achieve state-of-the-art performance.
  arXiv  Detail & Related papers  (2022-03-31T10:46:47Z)
• Generative hypergraph clustering: from blockmodels to modularity [26.99290024958576]
  We propose an expressive generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes. We show that hypergraph Louvain is highly scalable, including as an example an experiment on a synthetic hypergraph of one million nodes. We use our model to analyze different patterns of higher-order structure in school contact networks, U.S. congressional bill cosponsorship, U.S. congressional committees, product categories in co-purchasing behavior, and hotel locations.
  arXiv  Detail & Related papers  (2021-01-24T00:25:22Z)

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.