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Abstract:
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The dynamic (time-varying) evolution of groups in network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for clustering with this approach exist for dynamic networks, these methods currently assume a static community structure. This paper presents a nonparametric clustering model for dynamic networks that can model networks with an evolving group structure. Our model extends existing latent space approaches by explicitly modeling the addition, deletion, splitting and merging of groups with a hierarchical Dirichlet process hidden Markov model (HDP-HMM). Our proposed approach, the hierarchical Dirichlet process latent position clustering model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, is applicable to both directed and undirected networks, and avoids the expensive approximate BIC selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm, and apply this method to synthetic and real world networks to demonstrate its performance.
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