A comment regarding polynomial discriminant functions

The two papers abstracted above, the first by Duarte Silva and Stam and the second by Banks and Abad, do an excellent job of illustrating the potential value of expanding nontraditional discrimanant procedures, specifically those based on mathematical programming models, from first order to higher order polynomials in the observed attributes. Professors Duarte Silva and Stam give compelling evidence, through their experiments, that second order extensions of such methods, particularly the ‘hybrid’ model of Glover et al. can outperform traditional methods when the data departs significantly from the multivariable Gaussian family of distributions. Professors Banks and Abad reaffirm this by showing that their discriminant heuristics, applied to a quadratic transformation of the original data, outperform the quadratic discriminant function of Smith on selected samples of ‘real world’ data. In this note, the author wishes to offer a few brief comments regarding the implementation of polynomial discriminant procedures.