A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region

Abstract

A linear-programming model is proposed for deriving discriminant rules that allow allocation of entities to a reserved-judgment region. The size of the reserved-judgment region, which can be controlled by varying parameters within the model, dictates the level of aggressiveness (cautiousness) of allocating (misallocating) entities to groups. Results of simulation experiments for various configurations of normal and contaminated normal three-group populations are reported for a variety of parameter selections. Results of cross-validation experiments using real data sets are also reported. Both the simulation and cross-validation experiments include comparison with other discriminant analysis techniques. The results demonstrate that the proposed model is useful for deriving discriminant rules that reduce the chances of misclassification, while maintaining a reasonable level of correct classification.