Analysis of the Performance of a Parametric and Nonparametric Classification System: An Application to Feature Selection and Extraction in Radar Target Identification

摘要

This dissertation investigates new parametric and nonparametric bounds on the Bayes risk that can be used as a criterion in feature selection and extraction in radar target identification (RTI). For the parametric case, where the form of the underlying statistical distributions is known. Bayesian decision theory offers a well-motivated methodology for the design of parametric classifiers. This investigation provides new bounds on the Bayes risk for both simple and composite classes. Bounds on the Bayes risk for M classes are derived in terms of the risk functions for (M-1) classes, and so on until the result depends only on the Pairwise Bayes risks. When the parameters of the underlying distributions are unknown, an analysis of the effect of finite sample size and dimensionality on these bounds is given for the case of supervised learning. For the case of unsupervised learning, the parameters of these distributions are evalauted by using the maximum liklihood technique by means of an iterative method an appropriate algorithm. Finally, for the nonparametric case, where the form of the underlying statistical distributions is unkown, a nonparametric technique, the nearest-neighbor (N N) rule, is used to prrovide estimated bounds on the Bayes risk. Two methods are proposed to produce a finite sample size risk close to the asymptotic one. The difference between the finite sample size risk and the asympiotic risk is used as the criterion of improvement.