A Two-stage Algorithm for the Two Groups Classification Problem: A Combined LP-GP based Approach

Abstract

This paper presents a two-stage algorithm, which is totally different from the previous Discriminate Analysis (DA) approaches, to solve two groups classification problem. In contrast with other works in the literature of DA, we present an approach, called pre-estimating discriminate analysis (PDA), which can be able to minimize the number of misclassified observations and its deviations, simultaneously. In the first stage, we pre-estimate the minimum number of units which can be a misclassification; equivalently, we identify the minimum number of units that have a potential to be misclassification. We call these units potentially misclassified units. In the second stage, considering these potentially misclassified units and correct classified units obtained from previous stage, a linear classification boundary is obtained by solving a linear programming model. This linear model is designed to minimize sum deviations of the potentially misclassified units accompanying maximizing the total distances of the correct classified units.