  We study 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.
