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.
Cite
Text
Dall'Amico et al. "Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs." Neural Information Processing Systems, 2019.Markdown
[Dall'Amico et al. "Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs." Neural Information Processing Systems, 2019.](https://mlanthology.org/neurips/2019/dallamico2019neurips-revisiting/)BibTeX
@inproceedings{dallamico2019neurips-revisiting,
title = {{Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs}},
author = {Dall'Amico, Lorenzo and Couillet, Romain and Tremblay, Nicolas},
booktitle = {Neural Information Processing Systems},
year = {2019},
pages = {4037-4047},
url = {https://mlanthology.org/neurips/2019/dallamico2019neurips-revisiting/}
}