Multilayer-Dynamic Network Clustering with Application to World Trade Data

Abstract

International trade data, such as the FAO dataset, can be naturally represented as \emph{multilayer-dynamic networks}, where countries are nodes, trade relationships are edges, different products correspond to different layers, and networks evolve over time. An important problem is how to identify evolving community structures in such multilayer-dynamic trade networks. Motivated by this problem, we study community detection in multilayer-dynamic networks, allowing the community structure to vary across both layers and time. We propose a novel method, \emph{MuDySC} (Multilayer-Dynamic Spectral Clustering), which smooths the eigenspace projection matrices across adjacent time points and across layers at the same time point. We develop an efficient alternating iterative algorithm and establish both global and local convergence results, with the latter allowing weaker conditions on the tuning parameters when the relevant eigenspaces are sufficiently close and the algorithm is suitably initialized. We apply MuDySC to the FAO data. The analysis reveals clear asymmetry between export and import community structures and highlights both persistent and shifting trade positions of major countries. As an extension to accommodate substantial heterogeneity across network layers, we develop TLC-MuDySC, a tensor-based layer-clustering method that first identifies structurally related layers and then applies MuDySC within the estimated layer groups.