Some New Error Bounds and Approximations for Pattern Recognition

For the average error probability Pe associated with the Bayes recognition procedures for two possible patterns, using no context, new upper and lower bounds and approximations are obtained. Results are given in terms of simple functions of feature "reliability" and a priori probabilities of the patterns. Two kinds of feature "reliability" are considered, i.e., distance between probability distributions and error probabilities without the use of a priori probabilities. Computational advantages offered by those bounds and approximations are pointed out. The question as to how close they are to Peis examined. In some special cases, they are perfect. Numerical examples show that the differences are in general about 5-10 percent, and comparisons with certain known results are quite favorable. Possible applications are discussed. Extension is also made to m possible patterns arranged in a hierarchy with two elements at each branching.