MODEL-BASED CLUSTERING OF LARGE NETWORKS

• 成果类型: Article
• 署名作者: Vu, Duy Q.; Hunter, David R.; Schweinberger, Michael
• 署名单位: University of Melbourne; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Rice University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/12-AOAS617
• 发表日期: 2013
• 页码: 1010-1039
• 关键词: statistical-analysis; exponential family; bayesian-inference; social networks; graphs; distributions; prediction

摘要

We describe a network clustering framework, based on finite mixture models, that can be applied to discrete-valued networks with hundreds of thousands of nodes and billions of edge variables. Relative to other recent model-based clustering work for networks, we introduce a more flexible modeling framework, improve the variational-approximation estimation algorithm, discuss and implement standard error estimation via a parametric bootstrap approach, and apply these methods to much larger data sets than those seen elsewhere in the literature. The more flexible framework is achieved through introducing novel parameterizations of the model, giving varying degrees of parsimony, using exponential family models whose structure may be exploited in various theoretical and algorithmic ways. The algorithms are based on variational generalized EM algorithms, where the E-steps are augmented by a minorization-maximization (MM) idea. The bootstrapped standard error estimates are based on an efficient Monte Carlo network simulation idea. Last, we demonstrate the usefulness of the model-based clustering framework by applying it to a discrete-valued network with more than 131,000 nodes and 17 billion edge variables.