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February 2015 Consistency of spectral clustering in stochastic block models
Jing Lei, Alessandro Rinaldo
Ann. Statist. 43(1): 215-237 (February 2015). DOI: 10.1214/14-AOS1274


We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\log n$, with $n$ the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block models using a spherical $k$-median spectral clustering method. A key component of our analysis is a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality and may be of independent interest.


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Jing Lei. Alessandro Rinaldo. "Consistency of spectral clustering in stochastic block models." Ann. Statist. 43 (1) 215 - 237, February 2015.


Published: February 2015
First available in Project Euclid: 9 December 2014

zbMATH: 1308.62041
MathSciNet: MR3285605
Digital Object Identifier: 10.1214/14-AOS1274

Primary: 62F12

Keywords: network data , Sparsity , spectral clustering , Stochastic block model

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 1 • February 2015
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