A class of upper-bounds on probability of error for multi-hypotheses pattern recognition

A class of upper bounds on the probability of error for the general multihypotheses pattern recognition problem is obtained. In particular, an upper bound in the class is shown to be a linear functional of the pairwise Bhattacharya coefficients. Evaluation of the bounds requires knowledge of a-priori probabilities and of the hypothesis-conditional probability density functions. A further bound is obtained that is independent of apriori probabilities. For the case of unknown apriori probabilities and conditional probability densities, an estimate of the latter upper bound is derived using a sequence of classified samples and Kernel functions to estimate the unknown densities.