Estimation of the Posterior Probabilities of Classes by the Approximation of the Anderson Discriminant Function

Abstract

The approximation of the Anderson discriminant function at a given point in the feature space of two classes using a supervised training sample allows estimating the posterior probabilities of classes as easily as converting Fahrenheit degrees to Celsius degrees. These probabilities make it possible to further solve the classification problem with subjectively specified costs of classification errors and criteria. The training sample is simply converted to a regression analysis sample by replacing the class numbers with differences in error costs. A nonparametric method for approximating the discriminant function at a point is proposed. It does not require the specification of an approximation function at a point more complex than a linear one. Examples are given.