Sequential Low-Rank Change Detection
This work addresses the challenge of efficient low-rank change detection in high-dimensional applications like camera surveillance and swarm monitoring, offering an incremental improvement through sketching for dimensionality reduction.
The paper tackles the problem of detecting the emergence of a low-rank signal from high-dimensional data, such as in surveillance or sensor monitoring, by using a sketching-based approach with random Gaussian matrices to reduce dimensionality and analyzing the largest eigenvalue of the sample covariance matrix over a sliding window, achieving performance characterized by false-alarm-rate and expected detection delay.
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking.