TY - JOUR
T1 - A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks
AU - Loyal, Joshua Daniel
AU - Chen, Yuguo
N1 - ∗This work was supported in part by a grant from Sandia National Laboratories. †Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820, [email protected] ‡Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820, [email protected]
PY - 2023
Y1 - 2023
N2 - The evolution of communities in dynamic (time-varying) 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, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.
AB - The evolution of communities in dynamic (time-varying) 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, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.
KW - Longitudinal networks
KW - Mixture model
KW - Nonparametric bayes
KW - Social networks
KW - Statistical network analysis
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U2 - 10.1214/21-BA1300
DO - 10.1214/21-BA1300
M3 - Article
AN - SCOPUS:85144954962
SN - 1936-0975
VL - 18
SP - 49
EP - 77
JO - Bayesian Analysis
JF - Bayesian Analysis
IS - 1
ER -