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.