A piecewise linear programming approach to the two-group discriminant problem – an adaptation to Fisher's linear discriminant function model

Most existing linear programming (LP) models have optimization objectives that are very different from Fisher's linear discriminant function (FLDF). An LP technique that adapts to FLDF to solve the two-group classification problem is desirable, as FLDF is one of the most popular classification rules. Therefore, this paper introduces a piecewise linear programming (PLP-p) approach that has an optimization objective very similar to that of FLDF to solve the two-group classification problem in discriminant analysis. Moreover, the paper compares the classificatory performance between FLDF and the new PLP-p model, and shows that the results from both approaches are as good as each other when applied to three published data sets. However, the new PLP-p is more flexible than FLDF in terms of adding different types of constraints and weighting individual observations. The results of a simulation experiment confirm the value of our proposed approach.