Abstract
The main part of this paper is devoted to the systematic description of a best linear discriminant function (BLD). The geometrical relationship between a linear function and a multidimentional normal distribution is considered first to obtain the effctive index for calculating the total misclassification rate of a linear discriminant function. Then, the Pareto optimality is shown as the necessary condition for the BLD, which in turn enables the mathematical formulation of the BLD derivation as the optimization problem with one variable.
In the remained part, we propose the simple algorithm for obtaining the BLD which satisfies the minimax criterion. Convergence of the algorithm is proved.
