cea-01140852
https://cea.hal.science/cea-01140852
arxiv:1406.1880
[CEA] CEA - Commissariat à l'énergie atomique
[ESPCI] ESPCI ParisTech
[CNRS] CNRS - Centre national de la recherche scientifique
[PARISTECH] ParisTech
[LPCT] Laboratoire de Physico-Chimie Théorique
[DSM-IPHT] IPHT
[CEA-UPSAY] CEA - Université Paris-Saclay
[PSL] Université Paris sciences et lettres
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[CEA-UPSAY-SACLAY] CEA-UPSAY-SACLAY
[CEA-DRF] Direction de Recherche Fondamentale
[ESPCI-PSL] Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris - PSL
[GS-MATHEMATIQUES] Graduate School Mathématiques
[GS-PHYSIQUE] Graduate School Physique
Spectral Clustering of Graphs with the Bethe Hessian
Saade, Alaa
Krzakala, Florent
Zdeborová, Lenka
[PHYS] Physics [physics]
UNDEFINED
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.
2015-04-09
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