Statistics Papers

Document Type

Journal Article

Date of this Version

12-24-2013

Publication Source

PNAS

Volume

110

Issue

52

Start Page

20935

Last Page

20940

DOI

10.1073/pnas.1312486110

Abstract

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here, we present a class of spectral algorithms based on a nonbacktracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all of the way down to the theoretical limit. We also show the spectrum of the nonbacktracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.

Comments

At the time of publication, author Elchanan Mossel was affiliated with University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

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Date Posted: 27 November 2017

This document has been peer reviewed.