Mathematical programming models for piecewise-linear discriminant analysis

Mathematical programming (MP) discriminant analysis models are widely used to generate linear discriminant functions that can be adopted as classification models. Nonlinear classification models may have better classification performance than linear classifiers, but although MP methods can be used to generate nonlinear discriminant functions, functions of specified form must be evaluated separately. Piecewise-linear functions can approximate nonlinear functions, and two new MP methods for generating piecewise-linear discriminant functions are developed in this paper. The first method uses maximization of classification accuracy (MCA) as the objective, while the second uses an approach based on minimization of the sum of deviations (MSD). The use of these new MP models is illustrated in an application to a test problem and the results are compared with those from standard MCA and MSD models.