Online Structural Change-point Detection of High-dimensional Streaming Data via Sparse Spectral Graphical Models

Abstract

In complex systems, high-dimensional streaming data collected by sensors provides valuable insights into system states through the analysis of cross-correlation structures between entities. This paper introduces a novel online structural change-point detection methodology aimed at estimating the evolving cross-correlation structure of HD streaming data in real-time. Traditional methods for dynamic graphical modeling of system structures suffer from computational inefficiencies and tend to introduce fictitious dynamics when changes are sparse or absent. Existing approaches also face limitations in sequential change-point detection and real-time graphical representation. To address these challenges, our approach sequentially estimates the cross-correlation structure within sliding time windows by constructing sparse spectral graphical models that capture conditional dependencies in the frequency domain. The sparsity within each time window and the regularization between consecutive windows are achieved using the group LASSO penalty, and structural changes are monitored with an exponentially weighted moving average control chart, allowing for efficient and timely detection of state changes. The methodology is implemented using the Alternating Direction Method of Multipliers, facilitating real-time monitoring of system dynamics. The performance of the proposed methodology is demonstrated through simulations and case studies.