An upper bound on the probability of misclassification in terms of the affinity

A distribution-free upper bound is derived for the Bayes probability of misclassification in terms of Matusita´s measure of affinity of several distributions for the multihypothesis pattern recognition problem. It is shown that for the two-class problem the bound reduces to the Hudimoto-Kailath bound in terms of the Bhattacharyya coefficient. An additional upper bound is derived which is independent of the a priori probabilities of the pattern classes.