Sequential detection of low-rank changes using extreme eigenvalues
This work addresses the problem of timely change detection in covariance structures for applications like swarm monitoring, though it is incremental as it builds on existing random matrix theory and sliding window approaches.
The paper tackles the problem of detecting abrupt changes in signal covariance from white noise to a low-rank structure, presenting two sequential detection procedures based on extreme eigenvalues of the sample covariance matrix. It achieves accurate control of false-alarm rates and demonstrates good performance in real-world swarm behavior change detection.
We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sample covariance matrix. To control false-alarm-rate, we present an accurate theoretical approximation to the average-run-length (ARL) and expected detection delay (EDD) of the detection, leveraging the extreme eigenvalue distributions from random matrix theory and by capturing a non-negligible temporal correlation in the sequence of scan statistics due to the sliding window approach. Real data examples demonstrate the good performance of our method for detecting behavior change of a swarm.