Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models (SBMs), recent advancements have extended these models to handle dynamic and weighted networks, allowing for a more accurate representation of temporal variations in structure. Additional developments have introduced methods for detecting structural changes, such as shifts in community membership. However, limited attention has been paid to dynamic networks with variable population sizes, where nodes may enter or exit the network. To address this gap, we propose an extension of dynamic SBMs (dSBMs) that incorporates a birth-death process, enabling the statistical clustering of nodes in dynamic networks with evolving population sizes. This work makes three main contributions: (1) the introduction of a novel model for dSBMs with birth-death processes, (2) a framework for parameter inference and prediction of latent communities in this model, and (3) the development of an adapted Variational Expectation-Maximization (VEM) algorithm for efficient inference within this extended framework.

翻译：动态网络中的统计聚类旨在识别在网络随时间演化过程中，内部连接模式相似或相异的节点群组。早期研究主要集中于静态随机块模型（SBM），而近期进展已将这些模型扩展至处理动态和加权网络，从而能更准确地表征结构的时序变化。进一步的发展引入了检测结构变化的方法，例如社区成员关系的转变。然而，对于具有可变节点数量的动态网络——即节点可能加入或退出网络的情形——关注尚显不足。为填补这一空白，我们提出了一种动态随机块模型（dSBM）的扩展，该模型结合了生灭过程，使得在节点数量演化的动态网络中进行节点统计聚类成为可能。本工作主要有三项贡献：（1）提出了一种结合生灭过程的新型动态随机块模型；（2）为该模型中的参数推断和潜在社区预测提供了一个框架；（3）开发了一种改进的变分期望最大化（VEM）算法，以在此扩展框架内实现高效推断。