A Multiple Criteria and Multiple Constraints Mathematical Programming Model for Classification

Abstract

Mathematical programming has been widely used in data classification. A general strategy to build classifiers is to optimize a global objective function such as the square-loss function. However, in many real life situations, optimizing only one single objective function can hardly achieve a satisfactory classifier. Thus a series of models based on multiple criteria mathematical programming (MCMP) have been proposed recently, such as the multiple criteria linear programming (MCLP) model and the linear discriminant Analysis (LDA) model. In this paper, we argue that due to the inherent complexity of the real world data, multiple criteria mathematical programming may be also inadequate to identify a genuine classification boundary. Under this observation, we present a multiple criteria multiple constraints mathematical programming (MC2MP) model for classification. More specifically, we extend a most recent multiple criteria programming model, the MEMBV model, into a multiple constraints MEMBV model.