Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem

This paper proposes a new linear programming approach to solve the two-group classification problem in discriminant analysis. This new approach is based on an idea from cluster analysis that objects within the same group should be more similar than objects between groups. Consequently, it is desirable for the classification score of an object to be nearer to its mean classification score, but further from the mean classification score of the other group. This objective is accomplished by minimizing the total deviation of the classification scores of the objects from their group mean scores in a linear programming approach. When applied to an actual managerial problem and simulated data, the proposed linear programming approach performs well both in groups separation and group-membership predictions of new objects. Moreover, this new approach has an advantage of obtaining more stable classification function across different samples than most of the existing linear programming approaches.