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Unlike most existing hypergraph clustering approaches, which evolve functions defined on vertices or hyperedges, the proposed methodology evolves a pairwise dissimilarity between vertices and couples this evolution with an agglomerative hyperedge clustering process. The resulting iterative scheme generates a hierarchy of hyperedge mergers driven by the progressive deformation of the dissimilarity measure. To illustrate the behavior of the proposed framework, we consider both a synthetic hypergraph and a biomedical classification problem based on the Indian Liver Patient Dataset. In the biomedical application, the method achieves higher recall, precision, and F1-score than a K-means baseline for the considered experimental setting. While the medical case study serves as an illustrative application, the main contribution of this work lies in the formulation of an evolution-driven clustering methodology based on non-local nonlinear operators acting on pairwise dissimilarities. The results suggest that such evolution-based dissimilarity updates provide a promising alternative for hypergraph clustering and the analysis of complex datasets.<\/jats:p>","DOI":"10.1063\/5.0349918","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T12:51:33Z","timestamp":1789476693000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Hypergraph-based clustering via nonlocal nonlinear evolution operators"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5741-8289","authenticated-orcid":false,"given":"Ana","family":"Isabel Mu\u00f1oz","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Materials Science and Engineering, and Electronic Technology, Rey Juan Carlos University , Madrid, Spain and Research Center for Data Complex Networks & Cybersecurity Sciences, Rey Juan Carlos University, Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7954-6169","authenticated-orcid":false,"given":"Regino","family":"Criado","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Materials Science and Engineering, and Electronic Technology, Rey Juan Carlos University , Madrid, Spain and Research Center for Data Complex Networks & Cybersecurity Sciences, Rey Juan Carlos University, Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"issue":"4-5","key":"2026091508512652800_c1","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","article-title":"Complex networks: Structure and dynamics","volume":"424","year":"2006","journal-title":"Phys. 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