  Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit
timeseries data to a linear dynamical system. In doing so, DMD decomposes
dynamic data into spatially coherent modes that evolve in time according to
exponential growth/decay or with a fixed frequency of oscillation. A prolific
application of DMD has been to video, where one interprets the high-dimensional
pixel space evolving through time as the video plays. In this work, we propose
a simple and interpretable motion detection algorithm for streaming video data
rooted in DMD. Our method leverages the fact that there exists a correspondence
between the evolution of important video features, such as foreground motion,
and the eigenvalues of the matrix which results from applying DMD to segments
of video. We apply the method to a database of test videos which emulate
security footage under varying realistic conditions. Effectiveness is analyzed
using receiver operating characteristic curves, while we use cross-validation
to optimize the threshold parameter that identifies movement.
