A comparison of standard and two-stage mathematical programming discriminant analysis methods

Classification models can be developed using standard or two-stage mathematical programming (MP) discriminant analysis methods. In standard MP discriminant analysis methods, discriminant functions are generated by solving a single MP model. In two-stage MP methods, observations that are difficult to classify are identified in the first stage, with greater emphasis being given to these observations in the second stage MP model for discriminant function generation. In this paper, two two-stage methods are described and compared with two standard MP models, the model for minimisation of the sum of deviations and the model for maximisation of classification accuracy. The performance of these MP discriminant analysis methods and Fisher's linear discriminant analysis, a parametric statistical technique, is then evaluated on a published data set and on a number of simulated data sets.