A linear goal programming model for classification with non-monotone attributes

Classification function analysis concerns separating two or more groups of objects in a data set and allocating new objects to previously defined groups. Usually, a set of attribute weights are estimated and the classification decision of an object is based on the weighted sum of its attribute scores. Statistical linear discriminant analysis, logistic regression, and linear programming approaches to classification problems have been proposed to address this problem. However, monotonicity of the attribute scores with respect to the likelihood of belonging to one specific group is presumed by these approaches. This may not be realistic in many applications. In this paper, a linear goal programming approach with the ability to capture the non-monotonicity of some attribute scores in classification problems is proposed. Classification performances of this approach and other classification approaches are evaluated by a simulation experiment. The results are very encouraging for the proposed approach.