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June 2015 Role of normalization in spectral clustering for stochastic blockmodels
Purnamrita Sarkar, Peter J. Bickel
Ann. Statist. 43(3): 962-990 (June 2015). DOI: 10.1214/14-AOS1285

Abstract

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [ Stat. Comput. 17 (2007) 395–416]. Indeed, our experiments show that normalization improves prediction accuracy. In this paper, for the popular stochastic blockmodel, we theoretically show that normalization shrinks the spread of points in a class by a constant fraction under a broad parameter regime. As a byproduct of our work, we also obtain sharp deviation bounds of empirical principal eigenvalues of graphs generated from a stochastic blockmodel.

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Purnamrita Sarkar. Peter J. Bickel. "Role of normalization in spectral clustering for stochastic blockmodels." Ann. Statist. 43 (3) 962 - 990, June 2015. https://doi.org/10.1214/14-AOS1285

Information

Received: 1 October 2013; Revised: 1 November 2014; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1320.62150
MathSciNet: MR3346694
Digital Object Identifier: 10.1214/14-AOS1285

Subjects:
Primary: 62H30
Secondary: 60B20

Keywords: asymptotic analysis , networks , normalization , spectral clustering , stochastic blockmodel

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • June 2015
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