Lee Kevin H, Xue Lingzhou, Hunter David R
Department of Statistics, Western Michigan University, Kalamazoo, MI 49008, USA.
Department of Statistics, The Pennsylvania State University, University Park, PA 16802, USA.
J Multivar Anal. 2020 Jan;175. doi: 10.1016/j.jmva.2019.104540. Epub 2019 Sep 5.
Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect a set of nodes sharing similar connectivity patterns in time-evolving networks. Our work is primarily motivated by detecting groups based on interesting features of the time-evolving networks (e.g., stability). In this work, we propose a model-based clustering framework for time-evolving networks based on discrete time exponential-family random graph models, which simultaneously allows both modeling and detecting group structure. To choose the number of groups, we use the conditional likelihood to construct an effective model selection criterion. Furthermore, we propose an efficient variational expectation-maximization (EM) algorithm to find approximate maximum likelihood estimates of network parameters and mixing proportions. The power of our method is demonstrated in simulation studies and empirical applications to international trade networks and the collaboration networks of a large research university.
动态网络是描述随时间演变的复杂系统的通用语言，离散时间网络模型为各种应用提供了一种新兴的统计技术。在随时间演变的网络中检测出一组具有相似连通性模式的节点是一个基本的研究问题。我们的工作主要是基于检测随时间演变网络的有趣特征（例如稳定性）来进行分组。在这项工作中，我们基于离散时间指数族随机图模型为随时间演变的网络提出了一个基于模型的聚类框架，该框架同时允许对组结构进行建模和检测。为了选择组数，我们使用条件似然来构建一个有效的模型选择标准。此外，我们提出了一种高效的变分期望最大化（EM）算法来找到网络参数和混合比例的近似最大似然估计。我们方法的有效性在模拟研究以及对国际贸易网络和一所大型研究型大学的合作网络的实证应用中得到了证明。
