  In an era of ubiquitous large-scale streaming data, the availability of data
far exceeds the capacity of expert human analysts. In many settings, such data
is either discarded or stored unprocessed in datacenters. This paper proposes a
method of online data thinning, in which large-scale streaming datasets are
winnowed to preserve unique, anomalous, or salient elements for timely expert
analysis. At the heart of this proposed approach is an online anomaly detection
method based on dynamic, low-rank Gaussian mixture models. Specifically, the
high-dimensional covariances matrices associated with the Gaussian components
are associated with low-rank models. According to this model, most observations
lie near a union of subspaces. The low-rank modeling mitigates the curse of
dimensionality associated with anomaly detection for high-dimensional data, and
recent advances in subspace clustering and subspace tracking allow the proposed
method to adapt to dynamic environments. Furthermore, the proposed method
allows subsampling, is robust to missing data, and uses a mini-batch online
optimization approach. The resulting algorithms are scalable, efficient, and
are capable of operating in real time. Experiments on wide-area motion imagery
and e-mail databases illustrate the efficacy of the proposed approach.
