A Modified Super-Efficiency DEA Approach for Solving Multi-Groups Classification Problems

Abstract

Among the various discriminant analysis (DA) methods, researchers have investigated several directions in this area: statistics, econometrics, computer data mining technologies and mathematical programming. Recently, as a nonparametric mathematical programming approach, Data envelopment analysis has been applied in DA area and received great attention. In this paper, we propose a new discriminant approach based upon the relative distance measured by super-efficiency data envelopment analysis (DEA). This approach may generally avoid the drawbacks that usually occur in statistics discriminations of constructing function to determine a DMU's category. On the other hand, this approach may maintain discriminant capabilities by incorporating the non-parametric feature of DEA into DA. At the same time, it can also inherit the advantages of avoiding the process of dealing with different dimensional data in DEA. Our approach can be used to classify a sample's category by the discrimination results, even in the multiple-groups situation. Therefore, it can be applied to the discriminant analysis in various real-life cases.