Linear programming approaches to three-group discriminant analysis

As most of the previous work in linear programming approaches to discriminant analysis pertains to two-group situations, this paper attempts to extend the approach to the more-than-two-group case. Comparative results from using four different linear programming based discriminant analysis formulations vis-a-vis Fischer’s linear discriminant approach are presented. The analyses were performed using Fischer’s Iris Data and the results indicate that, in comparision with Fischer’s linear discriminant function, the three-group optimize-sum-of-distances approach was superior while the Freed and Glover three-group formulation performed equally well on a misclassification rate basis. In addition, the performance of the other LP based formulations was not significantly inferior. More importantly, the operationalization of the linear programming based approaches to the three-group case is demonstrated.