Change point detection in dynamic network via regularized tensor decomposition

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. © 2023 American Statistical Association and Institute of Mathematical Statistics.