Exponential Possibility Discriminant Analysis

Abstract

This paper deals with an exponential possibility distirbution and its application to discriminant analysis. First, possibility analysis based on exponential possibility distributions is discussed with possibility and necessity measures in contrast with statistical analysis. Second, the identification method for obtaining the possibility distribution from the given data is formulated. Then, using two possibility distributions, the possibility discriminant rule is obtained. Third, given two possibility distributions, the possibility disciriminant analysis is formulated by the possibility or the necessity measure. This problem of disciminant analysis can be described as finding a feature vector that minimizes the possibility or the necessity measure. This problem can be reduced to an eigenvalue problem. An unknown input can be classified by the possibility discriminant rule. Furthermore, this discriminant analysis is extented to the case where several unknown inputs are given. In this case, more clear classification might be obtained than one unknown input because of more information. Last, numerical examples are shown to illustrate our proposed methods.