A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis

A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. Although having its own right, this model may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions other techniques fail. Results on data sets from the literature and on data sets randomly generated show that this model is very effective in generating powerful discriminant functions.