Evaluation of the Posterior Probability of a Class with a Series of Anderson Discriminant Functions

Abstract

We propose a method of supervised estimation with a training set of the posterior probabilities of an object belonging to classes according to a collection of known values of its features. These probabilities represent comprehensive information for solving the classification problem. They allow to solve the classification problem under various criteria (maximum probability, minimum average cost of error, etc.), which are usually chosen subjectively. Our approach to solving this problem is based on the construction of a series of approximations of special discriminant functions at whose zero points the posterior probabilities of the classes are specified during their construction. The heuristic approximation algorithm of the discriminant function used in the neighborhood of zero values is a part of the method. In the method, there is no need for additional modifications such as the Platt’s calibrator for the method of support vector machines. We give model examples of applying the proposed approach and an example from medical diagnostics with real data.