On the Peaking of the Hughes Mean Recognition Accuracy: The Resolution of an Apparent Paradox

The peaking phenomenon of the Bayes recognition accuracy of pattern classifiers with unknown underlying statistics is addressed. It is shown that this effect, known as the Hughes paradox, arises from improper comparisons of statistically incomparable models. A formalization of the notion of comparability is introduced, and some of the results obtained in the literature are revisited in this context.