Abstract
This chapter presents experimental comparison between the optimal discriminate plane based on samples and general discriminant analysis. The optimal discriminant function (ODF) is obtained from the ratio between the population distribution functions of two groups. The boundary is determined by the likelihood, Bayes, and risk methods. When two population distributions are normal, ODF is of quadratic form. When their variance–covariance matrices are equal, it is of linear form. But in the general case about population distributions, the form of ODF is not definite. The chapter focuses on the form of the discriminant function that is confined to the linear function. The optimal function among the linear discriminant functions has been investigated. When two population distributions are normal, it coincides with Anderson-Bahadour linear discriminant function. When the variance–covariance matrices are equal, it coincides with ODF. The optimal linear discriminant functions about the general population distributions have also been investigated.
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