Year: 2015
Type: conference-paper
Abstract: We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where the number of edges is of the same order as the number of vertices. We propose a spectral method based on a generalization of the non-backtracking Hashimoto matrix into hypergraphs. We analyze its performance on a planted generative model and compare it with other spectral methods and with Bayesian belief propagation (which was conjectured to be asymptotically optimal for this model). We conclude that the proposed spectral method detects communities whenever belief propagation does, while having the important advantages to be simpler, entirely nonparametric, and to be able to learn the rule according to which the hyperedges were generated without prior information.
Authors: Maria Chiara Angelini, Francesco Caltagirone, Florent Krzakala, Lenka Zdeborova
Institutions: Sapienza University of Rome, Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, CEA Paris-Saclay - Etablissement de Saclay, CEA Paris-Saclay, Institut de Physique Théorique
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1900968552