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.
Related
- Structural Analysis of a Dynamic Multilayer Network via Matrix Autoregressive Models: A Case Study of International Interactions between Countries
- A latent space hidden Markov model for clustering views in longitudinal multilayer networks
- The use of sequence databases for taxonomic research in phytovirology and the application of factor analysis of correspondences to the clustering of geminiviruses
- Mixture-of-Finite-Mixtures Wishart Model for Clustering Covariance Matrices with an Application to Brain Functional Connectivity
- Nonparametric Hypothesis Testing of High-dimensional Clustering With Application to Single-cell RNA Data
BibTeX
@misc{huang2026multilayerdynamic,
title = {{Multilayer-Dynamic Network Clustering with Application to World Trade Data}},
author = {Mengze Huang and Wenqing Su and Shisong Wu and Xiao Guo and Hai Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.05770},
eprint = {2607.05770},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05770},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multilayer-Dynamic Network Clustering with Application to World Trade Data
AU - Mengze Huang
AU - Wenqing Su
AU - Shisong Wu
AU - Xiao Guo
AU - Hai Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.05770
UR - https://arxiv.org/abs/2607.05770
AB - 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.
ER -