Learning Hypergraphs From Signals With Dual Smoothness Prior

• URL: http://arxiv.org/abs/2211.01717v1
• Date: Thu, 3 Nov 2022 11:13:02 GMT
• Title: Learning Hypergraphs From Signals With Dual Smoothness Prior
• Authors: Bohan Tang, Siheng Chen, Xiaowen Dong
• Abstract summary: We propose a framework to infer meaningful hypergraph topologies from observed signals. Our proposed framework can efficiently infer meaningful hypergraph topologies from observed signals.
• Score: 32.57393976907129
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The construction of a meaningful hypergraph topology is the key to processing signals with high-order relationships that involve more than two entities. Learning the hypergraph structure from the observed signals to capture the intrinsic relationships among the entities becomes crucial when a hypergraph topology is not readily available in the datasets. There are two challenges that lie at the heart of this problem: 1) how to handle the huge search space of potential hyperedges, and 2) how to define meaningful criteria to measure the relationship between the signals observed on nodes and the hypergraph structure. In this paper, to address the first challenge, we adopt the assumption that the ideal hypergraph structure can be derived from a learnable graph structure that captures the pairwise relations within signals. Further, we propose a hypergraph learning framework with a novel dual smoothness prior that reveals a mapping between the observed node signals and the hypergraph structure, whereby each hyperedge corresponds to a subgraph with both node signal smoothness and edge signal smoothness in the learnable graph structure. Finally, we conduct extensive experiments to evaluate the proposed framework on both synthetic and real world datasets. Experiments show that our proposed framework can efficiently infer meaningful hypergraph topologies from observed signals.

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)
• Combating Bilateral Edge Noise for Robust Link Prediction [56.43882298843564]
  We propose an information-theory-guided principle, Robust Graph Information Bottleneck (RGIB), to extract reliable supervision signals and avoid representation collapse. Two instantiations, RGIB-SSL and RGIB-REP, are explored to leverage the merits of different methodologies. Experiments on six datasets and three GNNs with diverse noisy scenarios verify the effectiveness of our RGIB instantiations.
  arXiv  Detail & Related papers  (2023-11-02T12:47:49Z)
• Hypergraph Structure Inference From Data Under Smoothness Prior [46.568839316694515]
  We propose a method to infer the probability for each potential hyperedge without labelled data as supervision. We use this prior to derive the relation between the hypergraph structure and the node features via probabilistic modelling. Experiments on both synthetic and real-world data demonstrate that our method can learn meaningful hypergraph structures from data more efficiently than existing hypergraph structure inference methods.
  arXiv  Detail & Related papers  (2023-08-27T18:28:58Z)
• 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)
• DualHGNN: A Dual Hypergraph Neural Network for Semi-Supervised Node Classification based on Multi-View Learning and Density Awareness [3.698434507617248]
  Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. This paper proposes the Dual Hypergraph Neural Network (DualHGNN), a new dual connection model integrating both hypergraph structure learning and hypergraph representation learning simultaneously in a unified architecture.
  arXiv  Detail & Related papers  (2023-06-07T07:40:04Z)
• Deep Hypergraph Structure Learning [34.972686247703024]
  Learning on high-order correlation has shown superiority in data representation learning, where hypergraph has been widely used in recent decades. How to generate the hypergraph structure among data is still a challenging task. DeepHGSL is designed to optimize the hypergraph structure for hypergraph-based representation learning.
  arXiv  Detail & Related papers  (2022-08-26T10:00:11Z)
• 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)
• Community Detection in General Hypergraph via Graph Embedding [1.4213973379473654]
  We propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multi-hypergraph in a low-dimensional vector space.
  arXiv  Detail & Related papers  (2021-03-28T03:23:03Z)
• node2coords: Graph Representation Learning with Wasserstein Barycenters [59.07120857271367]
  We introduce node2coords, a representation learning algorithm for graphs. It learns simultaneously a low-dimensional space and coordinates for the nodes in that space. Experimental results demonstrate that the representations learned with node2coords are interpretable.
  arXiv  Detail & Related papers  (2020-07-31T13:14:25Z)

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.