A Class of Upper Bounds on Probability of Error for Multi-Hypotheses Pattern Recognition

摘要

A class of upper bounds on the probability of error for the general multi-hypotheses 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 a priori probabilities. For the case of unknown a priori probabilities and conditional probability densities, an estimate of the latter upper bound is derived using a sequence of classified samples and Kernel functions to destimate the unknown densities. (Author)