Hypergraph-based clustering via nonlocal nonlinear evolution operators

In this paper, we introduce a novel clustering framework for hypergraphs based on the evolution of pairwise dissimilarities through nonlinear and non-local discrete p-Laplacian-inspired operators in both isotropic and anisotropic formulations. 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.