Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs

Abstract : Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix H r = (r 2 − 1)I n + D − rA for sparse heterogeneous graphs (following the degree-corrected stochastic block model) in a two-class setting. For a specific value r = ζ, clustering is shown to be insensitive to the degree heterogeneity. We then study the behavior of the informative eigenvector of H ζ and, as a result, predict the clustering accuracy. The article concludes with an overview of the generalization to more than two classes along with extensive simulations on synthetic and real networks corroborating our findings.
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Contributor : Lorenzo Dall'Amico <>
Submitted on : Monday, January 6, 2020 - 4:47:45 PM
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Lorenzo Dall'Amico, Romain Couillet, Nicolas Tremblay. Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs. Thirty-third Conference on Neural Information Processing Systems, Dec 2019, Vancouver, Canada. ⟨hal-02429525⟩

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