Adaptive Pattern Recognition with Random Costs and Its Application to Decision Trees

Pattern recognition with unknown costs of classification is formulated as a problem of adaptively learning the optimal scheme starting from an ad hoc decision scheme. It is shown that unsupervised learning is adequate to compute converging estimates of the mean values of the MN random classification costs, one for each combination of M classes and N decisions. The quantities required for estimation are 1) the decision taken, 2) the outcome of the cost random variable corresponding to the unknown class and the implemented decision, and 3) the a posteriori probabilities of all the classes. Some of the variations of the above learning scheme are discussed. An application of the proposed methodology for adaptively improving the performance of pattern-recognition trees is presented along with simulation results.