Linear discrimination with symmetrical models

摘要

An alternative approach to Fisher's method of linear discrimination is examined. The quality criterion used in the examined method is sometimes called the perceptron criterion function. Just as the Bayesian optimality of the Fisher method is connected with assumptions about normality of the populations, the optimality of the examined method is connected with some symmetry conditions. The main subject of the paper is the analysis of these optimal conditions. Examples of the probability models which satisfy the conditions of optimality are also given.