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Choosing the number of groups in a latent stochastic blockmodel for dynamic networks

Published online by Cambridge University Press:  15 November 2018

RICCARDO RASTELLI Open the ORCID record for RICCARDO RASTELLI [Opens in a new window] ,
PIERRE LATOUCHE  and
NIAL FRIEL
RICCARDO RASTELLI
Affiliation:
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland (e-mail: riccardo.rastelli@ucd.ie)
PIERRE LATOUCHE
Affiliation:
Laboratoire MAP5, UMR CNRS 8145, Université Paris Descartes & Sorbonne Paris Cité, Paris, France (e-mail: pierre.latouche@univ-paris1.fr)
NIAL FRIEL
Affiliation:
School of Mathematics and Statistics and Insight: Centre for Data Analytics, University College Dublin, Dublin, Ireland (e-mail: nial.friel@ucd.ie)
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Abstract

Latent stochastic blockmodels are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between nodes are observed at a number of different times. In this paper, we propose a new Bayesian framework to characterize the construction of connections. We rely on a Markovian property to describe the evolution of nodes' cluster memberships over time. We recast the problem of clustering the nodes of the network into a model-based context, showing that the integrated completed likelihood can be evaluated analytically for a number of likelihood models. Then, we propose a scalable greedy algorithm to maximize this quantity, thereby estimating both the optimal partition and the ideal number of groups in a single inferential framework. Finally, we propose applications of our methodology to both real and artificial datasets.

Keywords

stochastic blockmodelsdynamic networksgreedy optimizationBayesian inferenceintegrated completed likelihood
Type
Research Article
Information
Network Science , Volume 6 , Issue 4 , December 2018 , pp. 469 - 493
Copyright
Copyright © Cambridge University Press 2018 

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