By Definition Undefined: Adventures in Anomaly (and Anomalous Change) Detection

This paper is a personal and purposefully idiosyncratic survey of issues, some technical and some philosophical, that arise in developing algorithms for the detection of anomalies and anomalous changes in hyperspectral imagery. The technical emphasis in anomaly detection is on modeling background clutter. For hyperspectral imagery this is a challenge because there are so many channels (the hyperspectral part) and because there is so much spatial structure (the imagery part). A wide range of models has been proposed for characterizing hyperspectral clutter: global and local models, Gaussian and non-Gaussian models, full-rank and subspace models, parametric and nonparametric models. And hybrid combinations, thereof. In discussing how these models relate to each other, an important theme will be characterizing the quality of a model in the absence of ground truth. The anomaly itself of more of a philosophical creature. It is a deviation from what is typical or expected. In general, the detection of anomalies is complicated by the fact that anomalies are rare and that anomalies tend to defy any kind of precise specification. One might even say of anomalies that they are, by definition, undefined.