A comparison of a robust mixed-integer approach to existing methods for establishing classification rules for the discriminant problem

Abstract

A nonparametric mixed-integer programming formulation to solve the classification problem in linear discriminant analysis is proposed. The classification performance of this formulation is compared to the MSD linear programming approach and two commonly used statistical methods, Fisher's linear discriminant function and the quadratic discriminant function. Using real data with highly nonnormal distributions the mixed-integer formulation is shown to outperform any of the other three approaches. To study the performance of the mixed-integer formulation systematically, a Monte Carlo simulation experiment is conducted, sampling from several different distributions. The results show that the mixed-integer formulation outperforms the other three approaches on the training samples, except when the variance-covariances are heterogeneous, in which case the quadratic function classifies better. When holdout samples are used to evaluate the relative performance, the mixed-integer approach classifies well when the data are highly discrete and the variance-covariances are homogeneous, but does not fare as well under other data conditions. Therefore, this study suggests that under certain conditions the mixed-integer approach is an attractive alternative to establish classification methods.