We develop a generalization fo the classical Wilcoxon-Mann-Whitney rank-based statistic which is relevant for high-dimensional statisitical pattern recognition applications. The common practice of considering ranked interpoint distances is generalized to point-to-subset distances. This generalization can improve performance characteristics such as discriminatory power. A recurrence for the exact distribution of this generalized Wilcoxon-Mann-Whitney (GMWM) statistic are obtained. Relationship to a class of generalized weighted (k,l) nearest-neighbors classifiers, utility, and experimental results for a Positron Emission Tomography (PET) data set are discussed.

(Joint work with Carey Priebe)