Online Change-Point Detection in High-Dimensional Covariance Structure with Application to Dynamic Networks
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One important task in online data analysis is detecting network change, such as dissociation of communities or formation of new communities. Targeting on this type of application, we develop an online change-point detection procedure in the covariance structure of high-dimensional data. A new stopping rule is proposed to terminate the process as early as possible when a network change occurs. The stopping rule incorporates spatial and temporal dependence, and can be applied to non-Gaussian data. An explicit expression for the average run length (ARL) is derived, so that the level of threshold in the stopping rule can be easily obtained with no need to run time-consuming Monte Carlo simulations. We also establish an upper bound for the expected detection delay (EDD), the expression of which demonstrates the impact of data dependence and magnitude of change in the covariance structure. Simulation studies are provided to confirm accuracy of the theoretical results. The practical usefulness of the proposed procedure is illustrated by detecting brain's network change in a resting-state fMRI dataset.
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