Convolutional Signal Propagation: A Simple Scalable Algorithm for Hypergraphs

• URL: http://arxiv.org/abs/2409.17628v1
• Date: Thu, 26 Sep 2024 08:22:09 GMT
• Title: Convolutional Signal Propagation: A Simple Scalable Algorithm for Hypergraphs
• Authors: Pavel Procházka, Marek Dědič, Lukáš Bajer,
• Abstract summary: This paper proposes Convolutional Signal Propagation (CSP), a non-parametric simple and scalable method that operates on bipartite graphs (hypergraphs) We show that CSP offers competitive performance while maintaining low computational complexity. Despite operating on hypergraphs, CSP achieves good results in tasks typically not associated with hypergraphs, such as natural language processing.
• Score: 0.13654846342364302
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Last decade has seen the emergence of numerous methods for learning on graphs, particularly Graph Neural Networks (GNNs). These methods, however, are often not directly applicable to more complex structures like bipartite graphs (equivalent to hypergraphs), which represent interactions among two entity types (e.g. a user liking a movie). This paper proposes Convolutional Signal Propagation (CSP), a non-parametric simple and scalable method that natively operates on bipartite graphs (hypergraphs) and can be implemented with just a few lines of code. After defining CSP, we demonstrate its relationship with well-established methods like label propagation, Naive Bayes, and Hypergraph Convolutional Networks. We evaluate CSP against several reference methods on real-world datasets from multiple domains, focusing on retrieval and classification tasks. Our results show that CSP offers competitive performance while maintaining low computational complexity, making it an ideal first choice as a baseline for hypergraph node classification and retrieval. Moreover, despite operating on hypergraphs, CSP achieves good results in tasks typically not associated with hypergraphs, such as natural language processing.

Related papers

• 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)
• NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification [70.51126383984555]
  We introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes. The efficient computation is enabled by a kernerlized Gumbel-Softmax operator. Experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs.
  arXiv  Detail & Related papers  (2023-06-14T09:21:15Z)
• Neural Graph Matching for Pre-training Graph Neural Networks [72.32801428070749]
  Graph neural networks (GNNs) have been shown powerful capacity at modeling structural data. We present a novel Graph Matching based GNN Pre-Training framework, called GMPT. The proposed method can be applied to fully self-supervised pre-training and coarse-grained supervised pre-training.
  arXiv  Detail & Related papers  (2022-03-03T09:53:53Z)
• SIGMA: A Structural Inconsistency Reducing Graph Matching Algorithm [21.1095092767297]
  We propose a novel criterion to measure the graph matching accuracy, structural inconsistency (SI) Specifically, SI incorporates the heat diffusion wavelet to accommodate the multi-hop structure of the graphs. We show that SIGMA can be derived by using a mirror descent method to solve the Gromov-Wasserstein distance with a novel K-hop-structure-based matching costs.
  arXiv  Detail & Related papers  (2022-02-06T15:18:37Z)
• HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering [9.438207505148947]
  We propose an efficient spectral hypergraph coarsening scheme (HyperSF) for preserving the original spectral (structural) properties of hypergraphs. Our results show that the proposed hypergraph coarsening algorithm can significantly improve the multi-way conductance of hypergraph clustering.
  arXiv  Detail & Related papers  (2021-08-17T22:20:23Z)
• A Robust and Generalized Framework for Adversarial Graph Embedding [73.37228022428663]
  We propose a robust framework for adversarial graph embedding, named AGE. AGE generates the fake neighbor nodes as the enhanced negative samples from the implicit distribution. Based on this framework, we propose three models to handle three types of graph data.
  arXiv  Detail & Related papers  (2021-05-22T07:05:48Z)
• Spatial-spectral Hyperspectral Image Classification via Multiple Random Anchor Graphs Ensemble Learning [88.60285937702304]
  This paper proposes a novel spatial-spectral HSI classification method via multiple random anchor graphs ensemble learning (RAGE) Firstly, the local binary pattern is adopted to extract the more descriptive features on each selected band, which preserves local structures and subtle changes of a region. Secondly, the adaptive neighbors assignment is introduced in the construction of anchor graph, to reduce the computational complexity.
  arXiv  Detail & Related papers  (2021-03-25T09:31:41Z)
• NetVec: A Scalable Hypergraph Embedding System [1.8979377273990425]
  We introduce NetVec, a novel framework for scalable un-supervised hypergraph embedding. We show that NetVec can becoupled with any graph embedding algorithm to produce embeddings of hypergraphs with millionsof nodes and hyperedges in a few minutes.
  arXiv  Detail & Related papers  (2021-03-09T18:06:56Z)
• Learning the Implicit Semantic Representation on Graph-Structured Data [57.670106959061634]
  Existing representation learning methods in graph convolutional networks are mainly designed by describing the neighborhood of each node as a perceptual whole. We propose a Semantic Graph Convolutional Networks (SGCN) that explores the implicit semantics by learning latent semantic-paths in graphs.
  arXiv  Detail & Related papers  (2021-01-16T16:18:43Z)
• Scalable Graph Neural Networks for Heterogeneous Graphs [12.44278942365518]
  Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark tasks. In this work, we ask whether these results can be extended to heterogeneous graphs, which encode multiple types of relationship between different entities.
  arXiv  Detail & Related papers  (2020-11-19T06:03:35Z)

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.