Further consideration of sample and feature size (Corresp.)

It is shown that in the context of a specific pattern classification decision metric the number of samples M needed to characterize a cluster described by N features is M \geq (1 + \beta^{-1})(N + 2) where \beta represents an interval width. The distance metric d^{2}(X)=(X-\hat{\mu}_{x})^{t}S_{x}^{-l}(X-\hat{\mu}_{x}) is shown to have an F -distribution which leads to the result for M . An additional application of the distribution of d^{2}(X) is discussed in terms of a specific type of pattern classifier.