A simple weighting scheme for classification in two-group discriminant problems

This paper introduces a new weighted linear programming model, which is simple and has strong intuitive appeal for two-group classifications. Generally, in applying weights to solve a classification problem in discriminant analysis where the relative importance of every observation is known, larger weights (penalties) will be assigned to those more important observations. The perceived importance of an observation is measured here as the willingness of the decision-maker to misclassify this observation. For instance, a decision-maker is least willing to see a classification rule that misclassifies a top financially strong firm to the group that contains bankrupt firms. Our weighted-linear programming model provides an objective-weighting scheme whereby observations can be weighted according to their perceived importance. The more important this observation, the heavier its assigned weight. Results of a simulation experiment that uses contaminated data show that the weighted linear programming model consistently and significantly outperforms existing linear programming and standard statistical approaches in attaining higher average hit-ratios in the 100 replications for each of the 27 cases tested.