Design and Development of Bayes' Minimax Linear Classification Systems

This paper considers the design and development of Bayes' minimax, linear classification systems using linear discriminant functions that are Bayes' equalizer rules. Bayes' equalizer rules divide two-class feature spaces into decision regions that have equal classification errors. I will formulate the problem of learning unknown linear discriminant functions from data as a locus problem, thereby formulating geometric locus methods within a statistical framework. Solving locus problems involves finding the equation of a curve or surface defined by a given property, and finding the graph or locus of a given equation. I will devise a system of locus equations that determines Bayes' equalizer rules which is based on a variant of the inequality constrained optimization problem for linear kernel support vector machines. Thereby, I will define a class of learning machines which are fundamental building blocks for Bayes' minimax pattern recognition systems.