Additional Features of an Adaptive, Multicategory Pattern Classification System

Some additional features of an adaptive, multicategory pattern classification system are presented. No a priori knowledge of the class probability densities or a priori probabilities of occurrence of the categories is required. The system utilizes a set of functions selected by the user to form discriminant functions. Adaptation of the system is accomplished using a set of independent pattern samples of known classification in such a manner that the system discriminant functions form minimum mean-square approximations to the Bayes discriminant functions as the number of samples of known classification increases. The convergence rate of the system is examined, and conditions are established under which the expected loss due to misclassification by the system is asymptotically equivalent to the minimum loss achievable when using the Bayes discriminant functions. In addition, a simulation of the system for a three-category problem is presented to demonstrate system performance for a finite number of adaptions.