Hypergraphs with edge-dependent vertex weights: p-Laplacians and spectral clustering

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dc.citation.articleNumber1020173en_US
dc.citation.journalTitleFrontiers in Big Dataen_US
dc.citation.volumeNumber6en_US
dc.contributor.authorZhu, Yuen_US
dc.contributor.authorSegarra, Santiagoen_US
dc.date.accessioned2023-03-23T14:10:36Zen_US
dc.date.available2023-03-23T14:10:36Zen_US
dc.date.issued2023en_US
dc.description.abstractWe study p-Laplacians and spectral clustering for a recently proposed hypergraph model that incorporates edge-dependent vertex weights (EDVW). These weights can reflect different importance of vertices within a hyperedge, thus conferring the hypergraph model higher expressivity and flexibility. By constructing submodular EDVW-based splitting functions, we convert hypergraphs with EDVW into submodular hypergraphs for which the spectral theory is better developed. In this way, existing concepts and theorems such as p-Laplacians and Cheeger inequalities proposed under the submodular hypergraph setting can be directly extended to hypergraphs with EDVW. For submodular hypergraphs with EDVW-based splitting functions, we propose an efficient algorithm to compute the eigenvector associated with the second smallest eigenvalue of the hypergraph 1-Laplacian. We then utilize this eigenvector to cluster the vertices, achieving higher clustering accuracy than traditional spectral clustering based on the 2-Laplacian. More broadly, the proposed algorithm works for all submodular hypergraphs that are graph reducible. Numerical experiments using real-world data demonstrate the effectiveness of combining spectral clustering based on the 1-Laplacian and EDVW.en_US
dc.identifier.citationZhu, Yu and Segarra, Santiago. "Hypergraphs with edge-dependent vertex weights: p-Laplacians and spectral clustering." <i>Frontiers in Big Data,</i> 6, (2023) Frontiers: https://doi.org/10.3389/fdata.2023.1020173.en_US
dc.identifier.digitalfdata-06-1020173en_US
dc.identifier.doihttps://doi.org/10.3389/fdata.2023.1020173en_US
dc.identifier.urihttps://hdl.handle.net/1911/114533en_US
dc.language.isoengen_US
dc.publisherFrontiersen_US
dc.rightsThis is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleHypergraphs with edge-dependent vertex weights: p-Laplacians and spectral clusteringen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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