Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels

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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.现代网络数据集通常由多个层级构成，形成共享同一组顶点（vertices）的网络集合，但各网络的连接模式可能存在差异。此类数据集需要足够灵活的模型与方法，既能捕捉不同网络间的局部与全局差异，同时又需具备统计简约性与可处理性，以得到计算高效、理论严谨且可跨网络聚合信息的解决方案。本文所研究的多层度校正随机块模型（multilayer degree-corrected stochastic blockmodel），假设一组网络共享相同的社区结构，但度校正项与块连接概率矩阵可各不相同。本文证明了该模型的可识别性，并提出了一种谱聚类（spectral clustering）算法。理论分析表明，即使存在显著的层级异质性，该算法的误聚类错误率（misclustering error rate）会随着多网络复现次数的增加呈指数级降低。仿真实验结果表明，在该挑战性场景下，本文方法的性能优于现有多层网络社区检测（multilayer community detection）方法。此外，针对2016年1月至2021年9月的美国机场数据集开展的案例研究显示，该方法能够识别出受疫情出行影响的机场热度变化趋势与具有实际意义的社区结构。本文的补充材料可在线获取，其中包含可用于复现研究工作的标准化材料说明。