Co-clustering Vertices and Hyperedges via Spectral Hypergraph Partitioning

• URL: http://arxiv.org/abs/2102.10169v1
• Date: Fri, 19 Feb 2021 21:47:39 GMT
• Title: Co-clustering Vertices and Hyperedges via Spectral Hypergraph Partitioning
• Authors: Yu Zhu, Boning Li, Santiago Segarra
• Abstract summary: We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent weights (EDVWs) In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a common space. We then cluster these embeddings to obtain our proposed co-clustering method, of particular relevance in applications requiring the simultaneous clustering of data entities and features.
• Score: 18.800058655626696
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented through an edge-dependent weight, conferring the model higher expressivity than the classical hypergraph. In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a common space. We then cluster these embeddings to obtain our proposed co-clustering method, of particular relevance in applications requiring the simultaneous clustering of data entities and features. Numerical experiments using real-world data demonstrate the effectiveness of our proposed approach in comparison with state-of-the-art alternatives.

Related papers

• Hyperbolic Delaunay Geometric Alignment [52.835250875177756]
  We propose a similarity score for comparing datasets in a hyperbolic space. The core idea is counting the edges of the hyperbolic Delaunay graph connecting datapoints across the given sets. We provide an empirical investigation on synthetic and real-life biological data and demonstrate that HyperDGA outperforms the hyperbolic version of classical distances between sets.
  arXiv  Detail & Related papers  (2024-04-12T17:14:58Z)
• 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)
• Hypergraphs with Edge-Dependent Vertex Weights: Spectral Clustering based on the 1-Laplacian [24.88719567631694]
  We propose a flexible framework for defining the 1-Laplacian of a hypergraph that incorporates edge-dependent weights. We show that for a special case within our framework, the corresponding hypergraph 1-Laplacian is equivalent to the 1-Laplacian of a related graph.
  arXiv  Detail & Related papers  (2023-04-30T12:21:42Z)
• Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clustering [29.400924845055865]
  We study p-Laplacians and spectral clustering for a recently proposed hypergraph model that incorporates edge-dependent weights (EDVWs) We convert hypergraphs with EDVWs into submodular hypergraphs for which the spectral theory is better developed. Existing concepts and theorems such as p-Laplacians and Cheeger inequalities proposed under the submodular hypergraph setting can be directly extended to hypergraphs with EDVWs.
  arXiv  Detail & Related papers  (2022-08-15T22:29:00Z)
• 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)
• 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)
• Spatial-Spectral Clustering with Anchor Graph for Hyperspectral Image [88.60285937702304]
  This paper proposes a novel unsupervised approach called spatial-spectral clustering with anchor graph (SSCAG) for HSI data clustering. The proposed SSCAG is competitive against the state-of-the-art approaches.
  arXiv  Detail & Related papers  (2021-04-24T08:09:27Z)
• 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)
• Hypergraph Random Walks, Laplacians, and Clustering [9.488853155989615]
  We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks. We show that the proposed methods produce higher-quality clusters and conclude by highlighting avenues for future work.
  arXiv  Detail & Related papers  (2020-06-29T20:58:15Z)
• 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.