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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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Jg. 79; H. 4; S. 1119 - 1141 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Oxford
Wiley
01.09.2017
Oxford University Press Royal Statistical Society |
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| ISSN: | 1369-7412, 1467-9868 |
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| Abstract | 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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| AbstractList | 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. 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. 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 (SBM) 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 behavior. We study identifiability of the model parameters , propose an inference procedure based on a variational expectation maximization algorithm as well as a model selection criterion to select for the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and compare our procedure with existing ones on synthetic datasets. We also illustrate our approach on dynamic contact networks, one of encounters among high school students and two others on animal interactions. An implementation of the method is available as a R package called dynsbm. |
| Author | Matias, Catherine Miele, Vincent |
| Author_xml | – sequence: 1 givenname: Catherine surname: Matias fullname: Matias, Catherine – sequence: 2 givenname: Vincent surname: Miele fullname: Miele, Vincent |
| BackLink | https://hal.science/hal-01167837$$DView record in HAL |
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| Copyright | 2016 Royal Statistical Society Copyright © 2017 The Royal Statistical Society and Blackwell Publishing Ltd Distributed under a Creative Commons Attribution 4.0 International License |
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| Keywords | stochastic block model variational expectation maximization contact network dynamic random graph graph clustering |
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| Snippet | Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and... Summary Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties... |
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| SubjectTerms | 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 |
| Title | Statistical clustering of temporal networks through a dynamic stochastic block model |
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