# Sequential detection of low-rank changes using extreme eigenvalues

## TL;DR

This paper introduces sequential change detection methods for identifying abrupt shifts in covariance matrices from identity to low-rank structures using extreme eigenvalues, with theoretical analysis and real data validation.

## Contribution

It proposes novel eigenvalue-based procedures for sequential change detection, incorporating accurate ARL and EDD approximations considering temporal correlations.

## Key findings

- Methods effectively detect covariance changes in real data.
- Theoretical approximations match empirical performance.
- Approach is robust for swarm behavior analysis.

## 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.