Advances in Operations Research
Volume 2009 (2009), Article ID 252989, 34 pages
doi:10.1155/2009/252989
Research Article

Mathematical Programming Approaches to Classification Problems

Soulef Smaoui,1 Habib Chabchoub,1 and Belaid Aouni2

1Unité de Recherche en Gestion Industrielle et Aide à la Décision, Faculté des Sciences Economiques et de Gestion, Sfax, Tunisia
2Decision Aid Research Group, School of Commerce and Administration, Faculty of Management, Laurentian University, Sudbury, ON, P3E2C6 , Canada

Received 22 March 2009; Revised 31 August 2009; Accepted 19 October 2009

Academic Editor: Mahyar Amouzegar

Copyright © 2009 Soulef Smaoui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variance-covariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decision-makers to choose the most appropriate model for their decision-making situation.