Çok Gruplu Sınıflandırma Problemlerine Regresyon Analizi ve Matematiksel Programlama Tabanlı Yeni Bir Yaklaşım

Mustafa İsa Doğan, Abdullah Orman, Mediha Örkcü, H. Hasan Örkcü
242 53

Öz


Bu çalışmada çok gruplu sınıflandırma problemlerinin çözümünde kullanılabilecek literatürde önerilen yöntemlerin bir kombinasyonu olan iki aşamalı yeni bir sınıflandırma yöntemi geliştirilmiştir. İlk aşamada, her bir birimin sınıflandırma skoru Satapathy ve diğ. [1]’e benzer bir şekilde her birim için oluşturulan doğrusal regresyon denklemi yardımıyla tahmin edilmektedir. İkinci aşamada, birimlerin sınıflandırılması eşik değer sınaması yapan matematiksel programlama modeli ile yapılmaktadır. Literatürden alınan 5 gerçek veri seti ve simülasyon çalışması sonuçlarından, önerilen yöntemin diğer çok gruplu matematiksel programlama tabanlı sınıflandırma yöntemlerine göre daha iyi performans gösterdiği gözlemlenmiştir.


Tam metin:

PDF


Referanslar


Satapathy, S.C., Murthy, J.V.R., Prasad Reddy, P.V.G.D., Misra, B.B., Dash, P.K., Panda, G., Particle swarm optimized multiple regression linear model for data classification, Applied Soft Computing, 9, 470-476, 2009.

Silva, A.P.D., Optimization approaches to Supervised Classification, European Journal of Operational Research, 261, 772–788, 2017.

Mahmoudi, N, Duman, E., Detecting credit card fraud by Modified Fisher Discriminant Analysis, Expert Systems with Applications, 42, 2510–2516, 2015.

Yagi, T., Takahashi, M., Business cycle turning points based on DEA discriminant analysis, Applied Economics, 48 (44), 4251-4256, 2016.

Benmalek, E., Elmhamdi, J., Jilbab, A. Multiclass classification of Parkinson’s disease using different classifiers and LLBFS feature selection algorithm. International Journal of Speech Technology, 20(1), 179–184, 2017.

Jing, Z., Wang, G., Zhang, S., Qiu, C., Building Tianjin driving cycle based on linear discriminant analysis, Transportation Research Part D, 53, 78–87, 2017.

Wilson, S.R., Close, M.E., Abraham, B., Applying linear discriminant analysis to predict groundwater redox conditions conducive to denitrification, Journal of Hydrology, 556, 611–624, 2018.

Chen, L., Wang, E.Y., Feng, J.J., Wang, X.R., Li, X.L., Hazard prediction of coal and gas outburst based on Fisher discriminant analysis, Geomechanics and Engıneering, 13 (5), 861-879, 2017.

Fisher, R., The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7 (2), 179-188, 1936.

Lachenburch P.A., Discriminant analysis, Hafner Press, New York, USA, 40-90, 1975.

Anderson, T.W., An introduction to multivariate analysis, Wiley, New York, USA, 10-25, 1984.

Fred, N., Glover, F., A Linear programming approach to the discriminant problem, Decision Sciences, 12, 68-74, 1981.

Fred, N., Glover, F., Simple but powerful goal programming formulations for the statistical discriminant problem, European Journal of Operational Research, 7, 44-60, 1981.

Markowski, E.P., Markowski, C.A., Some difficulties and improvements in applying linear programming formulations to the discriminant problem, Decision Sciences, 16, 237-247, 1985.

Fred, N., Glover, F., Evaluating alternative linear programming models to solve the two-group discriminant problem, Decision Sciences, 17, 151-162, 1986.

Fred, N., Glover, F., Resolving certain difficulties and improving the classification power of LP discriminant analysis formulations, Decision Sciences, 17, 589-595, 1986.

Joachimsthaler, E.A., Stam, A., Four approaches to the classification problem in discriminant analysis: An experimental study, Decision Sciences, 19, 322-333, 1988.

Koehler, G.J., Characterization of unacceptable solutions in LP discriminant analysis, Decision Sciences, 21, 239-257, 1989.

Koehler, G.J., Erenguc, S.S, Minimizing misclassifications in linear discriminant problem, Decision Sciences, 21, 63-85, 1990.

Glover, F., Improving linear programming models for the discriminant problem, Decision Sciences, 21, 771-785, 1990.

Rubin, A., A comparison of linear programming and parametric approaches to the two-group discriminant problem, Decision Sciences, 21, 373-386, 1990.

Lee, C.K., Ord, J.K., Disciminant analysis using least absolute deviations, Decision Sciences, 21, 86-96, 1990.

Stam, A., Jones, D.G., Classification performance of mathematical programming techniques in discriminant analysis: Results for small and medium sample sizes, Managerial and Decision Economics, 11, 243-253, 1990.

Stam, A., Ragsdale, C.T., On the classification gap in mathematical programming based approaches to the discriminant problem, Naval Research Logistic, 39, 545-559, 1992.

Hosseini, J.H., Armacost, R.L., Two-group discriminant problem with equal group mean vectors: An experimental evaluation of six linear/nonlinear programming formulations, European Journal of Operational Research, 77, 241-252, 1994.

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., An experimental comparison of some linear programming approaches to the discriminant problem, Computers and Operations Research, 24 (7), 593-599, 1997.

Lam, K.F., Moy, J.W., Combining discriminant method in solving classification problems in two-group discriminant analysis, European Journal of Operational Research, 138, 294-301, 2002.

Sueyoshi, T., DEA-Discriminant analysis in the view of goal programming, European Journal of Operational Research, 115, 564-582, 1999.

Sueyoshi, T., DEA-Discriminant Analysis: Extended DEA-Discriminant analysis, European Journal of Operational Research, 131, 324-351, 2001.

Sueyoshi, T., Mixed integer programming approach of extended DEA-Discriminant analysis, European Journal of Operational Research, 152, 45-55, 2004.

Sueyoshi, T., DEA-Discriminant analysis: Methodological comparison among eight discriminant analysis approaches, European Journal of Operational Research, 169, 247-272, 2006.

Bal, H., Örkcü, H.H., Çelebioğlu S., “An alternative model to Fisher and linear programming approaches in two-group classification problem: minimizing deviations from the group median”, G.U. Journal of Science, 19 (1), 49-55, 2006.

, 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.

Bal, H., Örkcü, H.H., “Data envelopment analysis approach to two-group classification problems and an experimantal comparison with some classification models”, Hacettepe Journal of Mathematics and Statistics, 36 (2), 169-180 , 2007.

Mai, Q., A review of discriminant analysis in high dimensions, WIREs Computational Statistics, 5, 190-197, 2013.

Carrizosa, E., Morales, D. R. Supervised classification and mathematical optimization. Computers and Operations Research, 40(1), 150–165, 2013.

Pendharkar, P.C., Troutt, M.D, Interactive classification using data envelopment analysis, Annals of Operations Research, 214, 125-141, 2014.

Bagirov, A. M., Kasimbeyli, R., Öztürk, G., Ugon, J. Piecewise linear classifiers based on nonsmooth optimization approaches. In T. M. Rassias, C. A. Floudas, & S. Butenko (Eds.), Optimization in Science and Engineering (pp. 1–32). New York, NY: Springer, 2014

Plastria, F., Carrizosa, E., Linear separation and approximation by minimizing the sum of concave functions of distances. 4OR-Q J Oper Res., 12, 77–85, 2014.

Astorino, A., Gaudioso, M., Seeger, A., Conic separation of finite sets in the homogeneous case, Journal of Convex Analysis, 21 (1), 1-28, 2014.

Tang, Y., Li, X., Xu, Y., Liu, S., Ouyang, S., A Mixed Integer Programming Approach to Maximum Margin 0 − 1 Loss Classification, IEEE International Radar conference (radar), (2014), 1-6.

Pavur, R., Loucopoulos, C., Examining optimal criterion weights in mixed integer programming approaches to the multi group classification problem, Journal of Operational Researh Society, 46, 626-640, 1995.

Gehrlein, W.W., General mathematical programming formulations for the statistical classification problem, Operations Research Letters, 5, 299-304, 1986.

Choo, E.U., Wedley, W.C., Optimal criterion weights in repetitive multicriteria decision making, Journal of Operational Research Society, 36, 983-992, 1985.

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.

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.

Gochet, W., Stam, A., Srinivisan, V., Chen, Shaoxiang, C., Multigroup discriminant analysis using linear programming, Operations Research, 45 (2), 213-225, 1997.

Bal, H., Örkcü, H.H. “A new mathematical programming approach to multi-group classification problems”, Computers and Operations Research, 38(1), 105-111, 2011.

Xu, G., Papageorgiou, L. G., A mixed integer optimisation model for data classification. Computers & Industrial Engineering, 56, 1205–1215, 2009.

Maskooki, A., Improving the efficiency of a mixed integer linear programming based approach for multi-class classification problem. Computers & Industrial Engineering, 66, 383–388, 2013.

Yang, L., Liu, S., Tsoka, S., Papageorgiou, L.G., Sample re-weighting hyper box classifier for multi-class data classification, Computers & Industrial Engineering, 85, 44–56, 2015.

Eberhart, R., Kennedy, J. A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on (pp. 39-43). IEEE, 1995.

Kennedy, J. Particle swarm optimization. In Encyclopedia of machine learning (pp. 760-766). Springer US, 2011.

Izadi, B., Ranjbarian, B., Ketabi, S., Nassiri-Mofakham, F., Performance analysis of classification methods and alternative linear programming integrated with fuzzy delphi feature selection. International Journal of Information Technology and Computer Science (IJITCS), 5(10), 9, 2013.

Zhang, Y., Yang, Y., Cross-validation for Selecting a Model Selection Procedure, Journal of Econometrics, 187, 95–112, 2015.

Vicente, T.F.Y., Hoai, M., Samaras, D., Leave-One-Out Kernel Optimization for Shadow Detection and Removal, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (3), 682-695, 2018.

Kim B., Oertzen, T.V., Classifiers as a model-free group comparison test, Behav Res., 50, 416–426, 2018.

Izadi, B., Ranjbarian, B., Ketabi, S., Performance Analysis of Classification Methods and Alternative Linear Programming Integrated with Fuzzy Delphi Feature Selection, I.J. Information Technology and Computer Science, 10, 9-20, 2013.

University of California-Irvine, www.ics.uci.edu/mlearn/MLRepository.html (2017).




Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.