Second order mathematical programming formulations for discriminant analysis

Abstract

This paper introduces a nonparametric formulation based on mathematical programming (MP) for solving the classification problem in discriminant analysis, which differs from previously proposed MP-based models in that, even though the final discriminant function is linear in terms of the parameters to be estimated, the formulation is quadratic in terms of the predictor (attribute) variables. Including second order (i.e., quadratic and cross-product) terms of the attribute variables in the model is similar in concept to the usual treatment of multiple predictor variables in statistical methods such as Fisher's linear discriminant analysis, and allows an analysis of how including nonlinear terms and interaction effects affect the predictive ability of the estimated classification function. Using simulation experiments involving data conditions for which nonlinear classifiers are appropriate, the classificatory performance of this class of second order MP models is compared with that of existing statistical (linear and quadratic) and first order MP-based formulations. The results of these experiments show that the proposed formulation appears to be a very attractive alternative to previously introduced linear and quadratic statistical and linear MP-based classification methods.