Year: 2016
Type: conference-paper
Abstract: We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal solution, and two spectral algorithms based on the non-backtracking and Bethe Hessian operators. For the case of two symmetric clusters, we conjecture that these algorithms are asymptotically optimal in that they detect the clusters as soon as it is information theoretically possible to do so. We substantiate this claim for one of the spectral approaches we introduce.
Institutions: École Normale Supérieure - PSL, Laboratoire de Physique de l'Ecole Normale Supérieure, Institut national de recherche en sciences et technologies du numérique, DYOGENE: Dynamics of Geometric Networks, Centre National de la Recherche Scientifique, Sorbonne Université, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, CEA Paris-Saclay - Etablissement de 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: W2295386361