Poster
Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs
Lorenzo Dall'Amico · Romain Couillet · Nicolas Tremblay
East Exhibition Hall B + C #73
Keywords: [ Algorithms; Algorithms -> Unsupervised Learning; Theory ] [ Statistical Physics of Learning ] [ Algorithms ] [ Clustering ]
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 Hr= (r^2−1)In+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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