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层结构构成，即基于同一组顶点构建多个网络的集合，但各网络的连接模式可能存在差异。这类数据需要足够灵活的模型与方法，既要能捕捉不同网络间的局部与全局差异，又要保持简约性与可处理性，从而得到计算高效且理论严谨的解决方案，实现跨网络的信息聚合。本文聚焦多层度校正随机块模型（multilayer degree-corrected stochastic blockmodel），该模型假设一组网络共享相同的社区结构，但允许度校正项与块连接概率矩阵存在差异。我们证明了该模型的可识别性，并提出了一种谱聚类算法。理论分析表明，即使存在显著的层间异质性，该算法的误聚类错误率会随多网络样本数量呈指数级下降。仿真实验结果显示，在该挑战性场景下，所提方法优于现有多层社区检测方法。此外，在针对2016年1月至2021年9月美国机场数据集的案例研究中，我们发现该方法能够识别出有意义的社区结构，以及疫情对出行影响下的机场热度变化趋势。本文的补充材料可在线获取，其中包含可复现研究成果的标准化材料说明。