Abstract
We present sequential change-point detection procedures based on linear sketches of high-dimensional signal vectors using generalized likelihood ratio (GLR) statistics. The GLR statistics allow for an unknown post-change mean that represents an anomaly or novelty. We consider both fixed and time-varying projections, derive theoretical approximations to two fundamental performance metrics: the average run length (ARL) and the expected detection delay (EDD); these approximations are shown to be highly accurate by numerical simulations. We further characterize the relative performance measure of the sketching procedure compared to that without sketching and show that there can be little performance loss when the signal strength is sufficiently large, and enough number of sketches are used. Finally, we demonstrate the good performance of sketching procedures using simulation and real-data examples on solar flare detection and failure detection in power networks.
Highlights
Online change-point detection from high-dimensional streaming data is a fundamental problem arising from applications such as real-time monitoring of sensor networks, computer network anomaly detection, and computer vision (e.g., [2, 3])
Our work is distinctive from the existing Statistical Process Control (SPC) charts using random projections in that (1) we developed new theoretical results for the sequential generalized likelihood ratio (GLR) statistic, (2) we consider the sparse 0-1 and time-varying projections, and (3) we study the amount of dimensionality reduction can be performed such that there is little performance loss
4 Results: Theoretical we present theoretical approximations to two performance metrics, the average run length (ARL), which captures the false alarm rate, and the expected detection delay (EDD), which captures the power of the detection statistic
Summary
Online change-point detection from high-dimensional streaming data is a fundamental problem arising from applications such as real-time monitoring of sensor networks, computer network anomaly detection, and computer vision (e.g., [2, 3]). A conventional approach is sketching (see, e.g., [4]), which performs random projection of the high-dimensional data vectors into lower-dimensional ones. We consider change-point detection using linear sketches of high-dimensional data vectors. Sketching reduces the computational complexity of the detection statistic from O(N) to O(M), where N is the original dimensionality and M is the dimensionality of sketches. Since we would like to perform real-time detection, any reduction in computational complexity (without incurring much performance loss) is highly desirable.
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