%0 Unpublished work
%T Spectral Clustering of Graphs with the Bethe Hessian
%+ Center for Soft Matter Research [New-York] (CSMR)
%+ Laboratoire de Physico-Chimie Théorique (LPCT)
%+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT)
%A Saade, Alaa
%A Krzakala, Florent
%A Zdeborová, Lenka
%Z 307087-SPARCS
%Z 8 pages, 2 figures
%Z t14/297
%8 2015-04-09
%D 2015
%Z 1406.1880
%Z Physics [physics]Preprints, Working Papers, ...
%X Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the non-backtracking walk on the graph, leads to improved performance in detecting clusters, and even to optimal performance for the stochastic block model. Here, we propose to use instead a simpler object, a symmetric real matrix known as the Bethe Hessian operator, or deformed Laplacian. We show that this approach combines the performances of the non-backtracking operator, thus detecting clusters all the way down to the theoretical limit in the stochastic block model, with the computational, theoretical and memory advantages of real symmetric matrices.
%G English
%L cea-01140852
%U https://cea.hal.science/cea-01140852
%~ CEA
%~ ESPCI
%~ CNRS
%~ PARISTECH
%~ LPCT
%~ DSM-IPHT
%~ CEA-UPSAY
%~ PSL
%~ UNIV-PARIS-SACLAY
%~ CEA-UPSAY-SACLAY
%~ CEA-DRF
%~ ESPCI-PSL
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE