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 parametr...

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Bibliographic Details
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
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Summary: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.
ISSN:0377-2217
1872-6860
DOI:10.1016/0377-2217(89)90390-1