A ratio model for discriminant analysis using linear programming

The innovative hybrid model for discriminant analysis via linear programming, was introduced along with the β normalization, which was subsequently replaced by a new normalization. The primary weakness of the β normalization, and the reason for replacing it with the new normalization, is that it distorts solutions and consequently does not always find the best solution. It is shown here, that unfortunately, both normalizations are affected by distance distortion. In addition, whether a model finds the best solution is highly dependent on the criterion or criteria by which ‘best solution’ is defined. A ratio criteria and associated ratio model are proposed, which avoid the problems associated with distance distortion. The nonlinear ratio may be linearized in much the same way that Data Envelopment Analysis is linearized.