Accession Number : AD0666900

Title :   ASYMPTOTICALLY OPTIMAL DISCRIMINANT FUNCTIONS FOR PATTERN RECOGNITION.

Descriptive Note : Technical rept.,

Corporate Author : TEXAS UNIV AUSTIN LABS FOR ELECTRONICS AND RELATED SCIENCE RESEARCH

Personal Author(s) : Wolverton,Charles T. ; Wagner,Terry J.

Report Date : 15 FEB 1968

Pagination or Media Count : 49

Abstract : The two category classification problem is considered. No a priori knowledge of the statistics of the classes is assumed. A sequence of labeled samples from the two classes is used to construct a sequence of approximations of a discriminant function which is optimum in the sense of minimizing the probability of misclassification but which requires knowledge of all the statistics of the classes. Depending on the assumptions made about the probability densities corresponding to the two classes, the integrated-square-error of the approximations converges in probability or with probability 1 to zero. The approximations are recursive and nonparametric. Rates of convergence are given. The approximations are used to define a decision procedure for classifying unlabeled samples. It is shown that as the number of labeled samples used to construct the approximations increases, the resulting sequence of discriminant functions is asymptotically optimal in the sense that the probability misclassification when using the approximations in the decision procedure converges in probability or with probability 1, depending on the assumptions made, to the probability misclassification of the optimum discriminant function. The results can be easily extended to the multicategory problem and to the case of an arbitrary Bayes risk (i.e., costs of misclassification not necessarily equal to 1). (Author)

Descriptors :   (*PATTERN RECOGNITION, *DECISION THEORY), SAMPLING, RANDOM VARIABLES, OPTIMIZATION, PROBABILITY, APPROXIMATION(MATHEMATICS), CONVERGENCE, INFORMATION THEORY, SET THEORY, ALGORITHMS, ADAPTIVE SYSTEMS, CLASSIFICATION, THEOREMS

Subject Categories : Operations Research
      Cybernetics
      Bionics

Distribution Statement : APPROVED FOR PUBLIC RELEASE