  In this work we consider the problem of detecting anomalous spatio-temporal
behavior in videos. Our approach is to learn the normative multiframe pixel
joint distribution and detect deviations from it using a likelihood based
approach. Due to the extreme lack of available training samples relative to the
dimension of the distribution, we use a mean and covariance approach and
consider methods of learning the spatio-temporal covariance in the low-sample
regime. Our approach is to estimate the covariance using parameter reduction
and sparse models. The first method considered is the representation of the
covariance as a sum of Kronecker products as in (Greenewald et al 2013), which
is found to be an accurate approximation in this setting. We propose learning
algorithms relevant to our problem. We then consider the sparse multiresolution
model of (Choi et al 2010) and apply the Kronecker product methods to it for
further parameter reduction, as well as introducing modifications for enhanced
efficiency and greater applicability to spatio-temporal covariance matrices. We
apply our methods to the detection of crowd behavior anomalies in the
University of Minnesota crowd anomaly dataset, and achieve competitive results.
