PhD thesis. This work was partly supported by the National Science Foundation under Grant ESC-85137020 and by IBM under the Resident Study Program.


This thesis is concerned with the design and evaluation of statistical classifiers. This problem has an optimal solution with a priori knowledge of the underlying probability distributions. Here, we examine the expected performance of parametric classifiers designed from a finite set of training samples and tested under various conditions. By investigating the statistical properties of the performance bias when tested on the true distributions, we have isolated the effects of the individual design components (i.e., the number of training samples, the dimensionality, and the parameters of the underlying distributions). These results have allowed us to establish a firm theoretical foundation for new design guidelines and to develop an empirical approach for estimating the asymptotic performance. Investigation of the statistical properties of the performance bias when tested on finite sample sets has allowed us to pinpoint the effects of individual design samples, the relationship between the sizes of the design and test sets, and the effects of a dependency between these sets. This, in turn, leads to a better understanding of how a single training set can be used most efficiently. In addition, we have developed a theoretical framework for the analysis and comparison of various performance evaluation procedures. Nonparametric and one-class classifiers are also considered. The reduced Parzen classifier, a nonparametric classifier which combines the error estimation capabilities of the Parzen density estimate with the computational feasibility of parametric classifiers, is presented. Also, the effect of the distance-space mapping in a one-class classifier is discussed through the approximation of the performance of a distance-ranking procedure.

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