An Alternative Model to Fisher and LinearProgramming Approaches in Two-Group Classification Problem: Minimizing Deviations from the Group Median (Review)

Year 2006, Volume: 19 Issue: 1, 49 - 55, 24.03.2010

Hasan Bal H.hasan Örkcü , Salih Çelebioğlu

Abstract

In this study, new classification models were developed which can be used in the solution to the problems of Discriminant Analysis having two groups. For the solution of these type of problems, Lam, Choo and Moy (1996) proposed a model regarding the minimization of deviations from the group means. The model examined by these authors loses its efficiency in respect of the hit ratio as the distributions of populations of samples considered go away from the normal distribution. For the samples drawn from non normal or skewed distributions, the median is a much more suitable descriptive statistic than the mean. The aim of the study is to consider the models of two-group classification problems by minimizing the deviations from the group medians. When these proposed approaches are applied to the data of real life or of simulation drawn from different distributions, it is observed that the attained performance of classification is better than both some important classification approaches in the literature and especially the classification performance minimizing the deviations from group means proposed by Lam, Choo and Moy.

 

 

Key Words: Statistical Discriminant Analysis, Goal Programming, median scores

Keywords

-

References

• Fred, N., Glover, F., “A linear programming approach to the discriminant problem”, Decision Sciences, 12: 68-74, (1981).
• Glover, F., “Improved Linear Programming Models for Discriminant Analysis”, Decision Sciences, 21: 771-785, (1990).
• Lam, K.F., Moy, J.W., “An experimental comparison of some recently developed linear programming approaches to the discriminant problem”, Computers and Operations Research, Vol: 24, No 7, 593-599, (1997).
• Lam, K.F., Moy, J.W., “Combining discriminant methods in solving classification problemsin two- group discriminant analysis”, European Journal of Operational Research, 138: 294-301, (2002).
• Lam, K.F., Choo, E.U., Moy, J.W., “Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem”, European Journal of Operational Research, 88, 358-367, (1996).
• Lam, K.F., Moy, J.W., “Improved Linear Programming Formulations for the Multi-group Discriminant Problem”, Journal of Operational Research Society, 47, 1526-1529, (1996).
• www.foreigntrade.gov.tr