Electronic Journal of Statistics

Classification and estimation in the Stochastic Blockmodel based on the empirical degrees

Antoine Channarond, Jean-Jacques Daudin, and Stéphane Robin

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The Stochastic Blockmodel [16] is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the distribution of the degrees concentrates in points conditionally on the node class. We show under a mild assumption that classification, estimation and model selection can actually be achieved with no more than the empirical degree data. We provide an algorithm able to process very large networks and consistent estimators based on it. In particular, we prove a bound of the probability of misclassification of at least one node, including when the number of classes grows.

Article information

Electron. J. Statist., Volume 6 (2012), 2574-2601.

First available in Project Euclid: 11 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62H12: Estimation

Stochastic Blockmodel unsupervised classification clustering estimation model selection


Channarond, Antoine; Daudin, Jean-Jacques; Robin, Stéphane. Classification and estimation in the Stochastic Blockmodel based on the empirical degrees. Electron. J. Statist. 6 (2012), 2574--2601. doi:10.1214/12-EJS753. https://projecteuclid.org/euclid.ejs/1357913089

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