Evaluating the maximize minimum distance formulation of the linear discriminant problem

• Published in: European journal of operational research 1989-07, Vol.41 (2), p.240-248
• Main Author: Rubin, Paul A.
• Format: Article
• Language: English
• Subjects: Applied sciences; Discriminant analysis; Exact sciences and technology; Linear programming; Mathematical models; Mathematical programming; Maximization; Minimization; Operational research and scientific management; Operational research. Management science; Operations research; Statistical analysis; statistics; Theory
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/0377-2217(89)90390-1

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. In this paper, we attribute the propensity of the MMD model to produce trivial solutions to a specific aspect of its formulation; this same facet may also cause unnessarily high misclassification rates even when a nontrivial function is found. We note a simple revision of a model which ensures an acceptable solution in those instancesin which the calibration samples can be classified with 100% accuracy by a single function. This rises 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.