Open Access
February 2016 Optimization via low-rank approximation for community detection in networks
Can M. Le, Elizaveta Levina, Roman Vershynin
Ann. Statist. 44(1): 373-400 (February 2016). DOI: 10.1214/15-AOS1360


Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to find communities, which is computationally infeasible. Some fast spectral algorithms have been proposed for specific methods or models, but only on a case-by-case basis. Here, we propose a general approach for maximizing a function of a network adjacency matrix over discrete labels by projecting the set of labels onto a subspace approximating the leading eigenvectors of the expected adjacency matrix. This projection onto a low-dimensional space makes the feasible set of labels much smaller and the optimization problem much easier. We prove a general result about this method and show how to apply it to several previously proposed community detection criteria, establishing its consistency for label estimation in each case and demonstrating the fundamental connection between spectral properties of the network and various model-based approaches to community detection. Simulations and applications to real-world data are included to demonstrate our method performs well for multiple problems over a wide range of parameters.


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Can M. Le. Elizaveta Levina. Roman Vershynin. "Optimization via low-rank approximation for community detection in networks." Ann. Statist. 44 (1) 373 - 400, February 2016.


Received: 1 May 2015; Revised: 1 July 2015; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1331.62312
MathSciNet: MR3449772
Digital Object Identifier: 10.1214/15-AOS1360

Primary: 62H30
Secondary: 62G20 , 62H25

Keywords: Community detection , social networks , spectral clustering , Stochastic block model

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • February 2016
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