We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal processing, machine learning, and data mining. Although most existing studies focus on the clustering of nodes in static graphs, we often encounter time-varying graphs for time-series data, e.g., social networks, brain functional connectivity, and point clouds. In this paper, we formulate a node clustering of time-varying graphs as an optimization problem based on spectral clustering, with a smoothness constraint of the node labels. We solve the problem with a primal-dual splitting algorithm. Experiments on synthetic and real-world time-varying graphs are performed to validate the effectiveness of the proposed approach.

翻译：我们提出一种针对时变图的节点聚类方法，其核心假设是聚类标签随时间平滑变化。聚类是信号处理、机器学习和数据挖掘等众多科学与工程领域的基础任务之一。尽管现有研究大多关注静态图中的节点聚类，但我们在处理时序数据（如社交网络、脑功能连接和点云数据）时经常面临时变图。本文基于谱聚类框架，将时变图的节点聚类问题建模为一个带节点标签平滑性约束的优化问题，并采用原始-对偶分裂算法进行求解。通过在合成数据与真实世界时变图上开展的实验，验证了所提方法的有效性。