Evaluating the maximize minimum distance formulation of the linear discriminant problem

The ‘maximize minimum distance’ (MMD) linear programming model for the two group discriminant problem has been noted to produce occasionally a trivial (identically zero) discriminant function, one which classifies all observations into a single category. In tests against other methods, both parametric and nonparametric, MMD has fared poorly. This paper attributes the propensity of the MMD model to produce trivial solutions to a specific aspect of its formulation; this same facet may also cause unnecessarily high misclassification rates even when a nontrivial function is found. It notes a simple revision of the model which ensures an acceptable solution in those instances in which the calibration samples can be classified with 100% accuracy by a single function. This raises the question of whether the inferior performance of MMD in previous studies was due to inherent limitations in MMD, or to the particular formulation used.