Change Point Detection in Dynamic Networks via Regularized Tensor Decomposition

Abstract

Dynamic network captures time-varying interactions among multiple entities at different time points, and detecting its structural change points is of central interest. This article proposes a novel method for detecting change points in dynamic networks by fully exploiting the latent network structure. The proposed method builds upon a tensor-based embedding model, which models the time-varying network heterogeneity through an embedding matrix. A fused lasso penalty is equipped with the tensor decomposition formulation to estimate the embedding matrix and a power update algorithm is developed to tackle the resultant optimization task. The error bound of the obtained estimated embedding matrices is established without incurring the computational-statistical gap. The proposed method also produces a set of estimated change points, which, coupled with a simple screening procedure, assures asymptotic consistency in change point detection under much milder assumptions. Various numerical experiments on both synthetic and real datasets also support its advantage. Supplementary materials for this article are available online.

KEYWORDS:

• Fused lasso
• Latent factor model
• Multi-layer network
• Network embedding
• Tensor power method

Supplementary Materials

Supplementary materials containing all the technical proofs, and the code and data for the numerical experiments are available online.

Acknowledgments

The authors are grateful to the associate editor and two anonymous referees, whose insightful comments and constructive suggestions have led to significant improvements in the article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

JZ’s research is supported in part by “USTC Research Funds of the Double First-Class Initiative” YD2040002020, YS’s research is supported in part by NSFC Grant 12171479 and the MOE Project of Key Research Institute of Humanities and Social Sciences 22JJD110001. JW’s research is supported in part by HK RGC Grants GRF-11304520, GRF-11301521, GRF-11311022, and CUHK Startup Grant 4937091.