Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels
针对多层网络数据，提出一种联合谱聚类算法，在共享社区结构但允许层间异质性的度修正随机块模型下，理论证明聚类误差随层数增加指数下降，并在美国机场数据中识别出受疫情影响的社区结构。
Modern network datasets are often composed of multiple layers, resulting in collections of networks over the same set of vertices but with potentially different connectivity patterns on each network. These data require models and methods that are flexible enough to capture local and global differences across the networks while at the same time being parsimonious and tractable to yield computationally efficient and theoretically sound solutions that are capable of aggregating information across the networks. This paper considers the multilayer degree-corrected stochastic blockmodel, where a collection of networks shares the same community structure, but degree corrections and block connection probability matrices are permitted to be different. We establish the identifiability of this model and propose a spectral clustering algorithm. Our theoretical results demonstrate that the misclustering error rate of the algorithm improves exponentially with multiple network realizations, even in the presence of significant layer heterogeneity. Simulation studies show that this approach improves on existing multilayer community detection methods in this challenging regime. Furthermore, in a case study of US airport data through January 2016 – September 2021, we find that this methodology identifies meaningful community structure and trends in airport popularity influenced by pandemic impacts on travel.