{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/submodular-hypergraphs-p-laplacians-cheeger","title":"Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering","arxiv_id":"1803.03833","date":"2018-03-10","proceeding":"ICML 2018 7","authors":["Pan Li","Olgica Milenkovic"],"abstract":"We introduce submodular hypergraphs, a family of hypergraphs that have\ndifferent submodular weights associated with different cuts of hyperedges.\nSubmodular hypergraphs arise in clustering applications in which higher-order\nstructures carry relevant information. For such hypergraphs, we define the\nnotion of p-Laplacians and derive corresponding nodal domain theorems and k-way\nCheeger inequalities. We conclude with the description of algorithms for\ncomputing the spectra of 1- and 2-Laplacians that constitute the basis of new\nspectral hypergraph clustering methods.","url_abs":"http://arxiv.org/abs/1803.03833v4","url_pdf":"http://arxiv.org/pdf/1803.03833v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"submodular-hypergraphs-p-laplacians-cheeger","repo_url":"https://github.com/lipan00123/IPM-for-submodular-hypergraphs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1803.03833","atlas_url":"https://app.syntology.ai/?focus=1803.03833","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}