A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR

Year 2011, Volume: 24 Issue: 1, 77 - 84, 14.01.2011

H.hasan Örkcü Hasan Bal

Abstract

In spite of the abundance of articles on mathematical programming models to the two-group classification problem, very few have addressed the multi-group classification problem using mathematical programming. This study presents a new multi-group data classification method based on mathematical programming. A new multi-group data classification model is proposed in this study that includes the strong properties of the mathematical programming models previously suggested for multi-group classification problems in the literature. The efficiency of proposed approach is tested on the well-known IRIS data set. The results on the IRIS data set show that our proposed method is usability and efficient on multi-group classification problems.

Keywords

-

References

• 1] Freed, N., Glover, F., “A linear programming approach to discriminant problem”, Decision Sciences, 12: 68–74 (1981a).
• [2] Freed, N., Glover, F., “Simple but powerful goal programming models for discriminant problems”, European Journal of Operational Research, 7: 44– 60 (1981b).
• [3] Fisher, R.A, “The use of multiple measurements in taxonomy problems”, Annals of Eugenics, 7: 179– 188 (1936).
• [4] Smith, C.A.B., “Some examples of discrimination”, Annals of Eugenics, 13: 272–282 (1947).
• [5] 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).
• [6] Sueyoshi, T., “DEA-discriminant analysis in the view of goal programming”, European Journal of Operational Research, 115: 564–582 (1999).
• [7] Sueyoshi, T., “DEA-Discriminant Analysis: Extended DEA-Discriminant analysis”, European Journal of Operational Research, 131: 324–351 (2001).
• [8] Sueyoshi, T., “Mixed integer programming approach of extended DEA-Discriminant Analysis”, European Journal of Operational Research, 152: 45–55 (2004).
• [9] Sueyoshi, T., “DEA-Discriminant Analysis: Methodological comparison among eight discriminant analysis approaches”, European Journal of Operational Research, 169: 247–272 (2006).
• [10] Glen, J.J., “A comparison of standard and two-stage mathematical programming discriminant analysis method”, European Journal of Operational Research, 171: 496–515 (2006).
• [11] Bal, H., Örkcü, H.H., Çelebioğlu S., “An experimental comparison of the new goal programming and linear programming approaches in the two-group discriminant problems”, Computers&Industrial Engineering, 50(3): 296– 311 (2006).
• [12] Bal, H., Örkcü, H.H., Çelebioğlu S., “An alternative model to Fisher linear programming approaches in two-group classification problem: Minimizing deviations from the group median”, G.U. Journal of Science, 19(1): 49–55 (2006).
• [13] Patwo, E., Hu, M.Y., Hung, M.S., “Two-group classification using neural networks”, Decision Sciences, 24(4): 825–845 (1993).
• [14] Holmstrom, L., Koistinen, P., Laaksonen, J., Oja, E., “Neural and statistical classifiers taxonomy and two case studies”, IEEE Trans. Neural Networks, 8: 5– 17 (1997).
• [15] Mangiameli, P., West, D., “An improved neural classification network for the two-group problem”, Computers and Operations Research, 26: 443–460 (1999)
• 16] Pendharkar, P.C., “A threshold varying artificial neural network approach for classification and its application to bankruptcy prediction problem”, Computers and Operations Research, 32: 2561– 2582 (2005).
• [17] Pavur, R., Loucopoulos, C., “Examining optimal criterion weights in mixed integer programming approaches to the multi group classification problem”, Journal of Operational Research Society, 46: 626–640 (1995).
• [18] Loucopoulos, C., Pavur, R., “Computational characteristics of a new mathematical programming model for the three-group discriminant problem”, Computers and Operations Research, 2: 179–191 (1997).
• [19] Gehrlein, W.V., “General mathematical programming formulations for the statistical classification problem”, Operations Research Letters, 5: 299–304 (1986).
• [20] Gochet, W., Stam, A., Srinivisan, V., Chen, Shaoxiang, C., “Multigroup discriminant analysis using linear programming”, Operations Research, 45(2): 213–225 (1997).
• [21] Östermark, R., Höglund, R., “Addressing the multigroup discriminant problem using multivariate statistics and mathematical programming”, European Journal of Operational Research, 108: 224–237 (1998).
• [22] Patterson, D.W., Artificial Neural Networks, Prentice Hall, Singapore, (1996).
• [23] Sexton, S.R., Dorsey, R.E., “Reliable classification using neural networks: a genetic algorithm and backpropagation comparison”, Decision Support Systems, 30: 11–22 (2000).
• [24] Rumelhart, D.E., Hinton, G., Williams, R., “Learning representation by back-propagation errors”, Nature, 323(9): 533-536 (1986).