On the binary classification problem in discriminant analysis using linear programming methods

Abstract

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.