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.
Recommended Citation
Krzakala, F., Moore, C., Mossel, E., Neeman, J., Sly, A., Zdeborová, L., & Zhang, P. (2013). Spectral Redemption in Clustering Sparse Networks. PNAS, 110 (52), 20935-20940. http://dx.doi.org/10.1073/pnas.1312486110
Included in
Statistical, Nonlinear, and Soft Matter Physics Commons, Statistics and Probability Commons
Date Posted: 27 November 2017
This document has been peer reviewed.
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.