基于层次距离矩阵的网络层次聚类
Hierarchical Clustering of Networks via Hierarchical Distance Matrices
AI总结：
该研究提出NHC-TST方法，通过层次距离矩阵框架实现网络群体的自适应层次聚类，在模拟和全球迁移数据集上均展现出良好的聚类与层次关系恢复能力。
AI中文摘要：
对网络群体进行聚类并恢复其潜在的层次结构是网络分析中一个基础性但尚未充分探索的问题。为将该问题形式化，我们引入层次距离矩阵（Hierarchical Distance Matrix），这是一类群体层面的距离矩阵，通过递归嵌套的距离分离编码潜在层次结构，可适配不平衡的树深度。基于该框架，我们提出一种完全数据驱动的自顶向下方法：基于两样本检验的网络层次聚类（NHC-TST）。该算法通过谱聚类递归划分网络，并采用基于图的两样本停止规则，可自适应确定分支结构，无需预先知晓聚类数量或树深度。理论上，我们证明了群体层面层次结构的精确恢复以及经验过程的统计一致性。模拟研究表明，在广泛设置下，该方法能高度准确地恢复聚类成员关系和层次关系。将其应用于全球迁移数据集时，NHC-TST 揭示了传统平面聚类方法未发现的、可解释的多分辨率时间结构。
英文摘要：
Clustering populations of networks while recovering their latent hierarchical organization is a fundamental yet largely unexplored problem in network analysis. To formalize this, we introduce the Hierarchical Distance Matrix, a specific class of population-level distance matrices that encodes latent hierarchical organization through recursively nested distance separation, accommodating unbalanced tree depths. Building on this framework, we propose a fully data-driven top-down procedure: network hierarchical clustering based on two-sample testing (NHC-TST). The algorithm recursively splits networks via spectral clustering and uses a graph-based two-sample stopping rule. The procedure adaptively determines the branching structure without requiring prior knowledge of the number of clusters or tree depth. Theoretically, we establish exact recovery of the population-level hierarchical structure and statistical consistency in the empirical procedure. Simulation studies demonstrate highly accurate recovery of both cluster memberships and hierarchical relationships across a wide range of settings. Applied to a global migration dataset, NHC-TST uncovers interpretable multi-resolution temporal structures that are not revealed by conventional flat clustering approaches.
