  Automatic detection of anomalies in space- and time-varying measurements is
an important tool in several fields, e.g., fraud detection, climate analysis,
or healthcare monitoring. We present an algorithm for detecting anomalous
regions in multivariate spatio-temporal time-series, which allows for spotting
the interesting parts in large amounts of data, including video and text data.
In opposition to existing techniques for detecting isolated anomalous data
points, we propose the "Maximally Divergent Intervals" (MDI) framework for
unsupervised detection of coherent spatial regions and time intervals
characterized by a high Kullback-Leibler divergence compared with all other
data given. In this regard, we define an unbiased Kullback-Leibler divergence
that allows for ranking regions of different size and show how to enable the
algorithm to run on large-scale data sets in reasonable time using an interval
proposal technique. Experiments on both synthetic and real data from various
domains, such as climate analysis, video surveillance, and text forensics,
demonstrate that our method is widely applicable and a valuable tool for
finding interesting events in different types of data.
