Statistical clustering of temporal networks through a dynamic stochastic block model

• 成果类型: Article
• 署名作者: Matias, Catherine; Miele, Vincent
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; VetAgro Sup
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12200
• 发表日期: 2017
• 页码: 1119-1141
• 关键词: maximum-likelihood; Mixture Model; Identifiability; inference

摘要

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.