Statistical clustering of temporal networks through a dynamic stochastic block model

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model for its static part with independent Markov chains for the evolution of...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 79; no. 4; pp. 1119 - 1141
Main Authors: Matias, Catherine, Miele, Vincent
Format: Journal Article
Language:English
Published: Oxford Wiley 01.09.2017
Oxford University Press
Royal Statistical Society
Subjects:
algorithms
animals
Binary data
Clustering
Contact network
data collection
Discrete time
Dynamic random graph
equations
Graph clustering
Graphs
Group dynamics
Groups
high school students
Inference
Markov analysis
Markov chain
Markov chains
Mathematics
Networks
Parameter identification
Property
Regression analysis
Secondary school students
Secondary schools
Statistical inference
Statistical methods
Statistics
Stochastic block model
Stochastic models
Switching theory
Time
Variational expectation–maximization
stochastic block model
variational expectation maximization
contact network
dynamic random graph
graph clustering
ISSN:1369-7412, 1467-9868
Online Access:Get full text
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Summary:Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model for its static part with independent Markov chains for the evolution of the nodes groups through time.We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within-group connectivity behaviour. We study identifiability of the model parameters and propose an inference procedure based on a variational expectation–maximization algorithm as well as a model selection criterion to select the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and we compare our procedure with existing procedures on synthetic data sets.We also illustrate our approach on dynamic contact networks: one of encounters between high school students and two others on animal interactions. An implementation of the method is available as an R package called dynsbm.
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12200