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Stochastic block models for multiplex networks: an application to a multilevel network of researchers
Author(s) -
Barbillon Pierre,
Donnet Sophie,
Lazega Emmanuel,
BarHen Avner
Publication year - 2017
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12193
Subject(s) - stochastic block model , connection (principal bundle) , consistency (knowledge bases) , computer science , cluster analysis , block (permutation group theory) , theoretical computer science , data mining , mathematics , artificial intelligence , geometry
Summary Modelling relationships between individuals is a classical question in social sciences and clustering individuals according to the observed patterns of interactions allows us to uncover a latent structure in the data. The stochastic block model is a popular approach for grouping individuals with respect to their social comportment. When several relationships of various types can occur jointly between individuals, the data are represented by multiplex networks where more than one edge can exist between the nodes. We extend stochastic block models to multiplex networks to obtain a clustering based on more than one kind of relationship. We propose to estimate the parameters—such as the marginal probabilities of assignment to groups (blocks) and the matrix of probabilities of connections between groups—through a variational expectation–maximization procedure. Consistency of the estimates is studied. The number of groups is chosen by using the integrated completed likelihood criterion, which is a penalized likelihood criterion. Multiplex stochastic block models arise in many situations but our applied example is motivated by a network of French cancer researchers. The two possible links (edges) between researchers are a direct connection or a connection through their laboratories. Our results show strong interactions between these two kinds of connection and the groups that are obtained are discussed to emphasize the common features of researchers grouped together.