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The generic problem in anomaly detection is identifying unusual samples present in a large population. Each member of the population is described by a list of characteristics that define a feature vector. One statistical method that accounts for mutual correlations among the components has defined the standard for anomaly detection in communication, radar, and hyperspectral signal processing for several decades. This paper describes an advanced methodology that constructs nonlinear transformations to account for observed data distributions not amenable to a statistical description. The construction relies on a combination of stochastic methods and phenomenological constraints. Examples are taken from hyperspectral target detection.