Dynamic clustering for heterophilic stochastic block models with time-varying node memberships
针对节点随时间逐渐改变成员关系的网络序列，提出核去偏平方和方法，通过去偏平方和聚合邻接矩阵后进行谱聚类，实现每个网络的社区一致检测，尤其适用于异配网络。
Summary We consider a time-ordered sequence of networks stemming from stochastic block models in which nodes gradually change their membership over time, and no network at any single time-point contains sufficient signal strength to recover its community structure. To estimate the time-varying community structure, we develop the kernel-debiased sum of squares method that performs spectral clustering after a debiased sum-of-squared aggregation of adjacency matrices. Our theory demonstrates, via a novel bias-variance decomposition, that our new method achieves consistent community detection in each network, even for heterophilic networks, without requiring smoothness in the time-varying dynamics of between-community connectivities. We also prove the identifiability of aligning community structures across time based on how rapidly nodes change communities, and we develop a data-adaptive bandwidth-tuning procedure for our new method. We demonstrate the utility and advantages of our proposed method through simulations and a novel analysis of time-varying dynamics in gene coordination in the human developing brain.