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A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR

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

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.

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

Abstract

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).
There are 24 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

H.hasan Örkcü

Hasan Bal

Publication Date January 14, 2011
Published in Issue Year 2011 Volume: 24 Issue: 1

Cite

APA Örkcü, H., & Bal, H. (2011). A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR. Gazi University Journal of Science, 24(1), 77-84.
AMA Örkcü H, Bal H. A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR. Gazi University Journal of Science. January 2011;24(1):77-84.
Chicago Örkcü, H.hasan, and Hasan Bal. “A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR”. Gazi University Journal of Science 24, no. 1 (January 2011): 77-84.
EndNote Örkcü H, Bal H (January 1, 2011) A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR. Gazi University Journal of Science 24 1 77–84.
IEEE H. Örkcü and H. Bal, “A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR”, Gazi University Journal of Science, vol. 24, no. 1, pp. 77–84, 2011.
ISNAD Örkcü, H.hasan - Bal, Hasan. “A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR”. Gazi University Journal of Science 24/1 (January 2011), 77-84.
JAMA Örkcü H, Bal H. A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR. Gazi University Journal of Science. 2011;24:77–84.
MLA Örkcü, H.hasan and Hasan Bal. “A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR”. Gazi University Journal of Science, vol. 24, no. 1, 2011, pp. 77-84.
Vancouver Örkcü H, Bal H. A COMBINING MATHEMATICAL PROGRAMMING METHOD FOR. Gazi University Journal of Science. 2011;24(1):77-84.