%0 Unpublished work %T Spectral Clustering of Graphs with the Bethe Hessian %+ Center for Soft Matter Research [New-York] (CSMR) %+ Laboratoire de Physico-Chimie Théorique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