Boundary Methods for Distribution Analysis

In this chapter we introduce the use of Boundary Methods (BM) for distribution analysis. We view these methods as tools which can be used to extract useful information from sample distributions. We believe that Boundary Methods can be used for a number of applications, but here we restrict our attention to three applications. First, we discuss the use of boundary methods for determining the suitability of a particular feature set for pattern classification, i.e. we use the Boundary Methods to perform feature-set evaluation (FSE). We present results which establish the correspondence of Boundary Methods and the probability of error (Pe) for normal distributions. Second, we discuss the utility of Boundary Methods as a technique for sample-pruning (SP), and show how we can select samples, e.g., for progressive training of neural-networks. Finally, we state a theorem which relates Fisher’s Linear Discriminant (FLD) and Boundary Methods.