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.