Title: Sequential detection of low-rank changes using extreme eigenvalues,
Abstract: 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.