Spectral Clustering of Graphs with the Bethe Hessian

Abstract : 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.
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https://hal-cea.archives-ouvertes.fr/cea-01140852
Contributor : Emmanuelle de Laborderie <>
Submitted on : Thursday, April 9, 2015 - 4:32:51 PM
Last modification on : Wednesday, August 14, 2019 - 10:46:02 AM

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  • HAL Id : cea-01140852, version 1
  • ARXIV : 1406.1880

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Alaa Saade, Florent Krzakala, Lenka Zdeborová. Spectral Clustering of Graphs with the Bethe Hessian. 2015. ⟨cea-01140852⟩

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