Abstract
We study the problem of community detection in multilayer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, that is, mixture multilayer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multilayer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.
Funding Statement
Jing and Li’s research is partially supported by the HK RGC Grants GRF 16304419 and GRF 16305616. Lyu and Xia’s research is partially supported by the HK RGC Grant ECS 26302019, GRF Grant 16303320 and WeBank-HKUST project WEB19EG01-g.
Acknowledgments
The authors thank the Editor, Associate Editor and four anonymous referees for their constructive comments on an earlier version of the manuscript.
Funding Statement
Jing and Li’s research is partially supported by the HK RGC Grants GRF 16304419 and GRF 16305616. Lyu and Xia’s research is partially supported by the HK RGC Grant ECS 26302019, GRF Grant 16303320 and WeBank-HKUST project WEB19EG01-g.
Acknowledgments
The authors thank the Editor, Associate Editor and four anonymous referees for their constructive comments on an earlier version of the manuscript.
Citation
Bing-Yi Jing. Ting Li. Zhongyuan Lyu. Dong Xia. "Community detection on mixture multilayer networks via regularized tensor decomposition." Ann. Statist. 49 (6) 3181 - 3205, December 2021. https://doi.org/10.1214/21-AOS2079
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