On the classification gap in mathematical programming‐based approaches to the discriminant problem

This article proposes a mathematical‐programming‐based approach to solve the classification problem in discriminant analysis which explicitly considers the classification gap. The procedure consists of two distinct phases and initially treats the classification gap as a fuzzy set in which the classification rule is not yet established. The nature of the classification gap is examined and a variety of methods are discussed which can be applied to identify the most appropriate classification rule over the fuzzy set. The proposed methodology has several potential advantages. First, it offers a more refined approach to the classification problem, facilitating careful analysis of the fuzzy region where the classification decision may not be obvious. Secondly, the two‐phase approach enables the analysis of larger data sets when using computer‐intensive procedures such as mixed‐integer programming. Finally, because of the restricted choice of separating hyperplanes in phase 2, the approach appears to be more robust than other classification techniques with respect to outlier‐contaminated data conditions. The robustness issue and computational advantage of our proposed methodology are illustrated using a limited simulation experiment.