Abstract
Nonlinear classification models have better classification performance than the linear classifiers. However, for many nonlinear classification problems, piecewise-linear discriminant functions can approximate nonlinear discriminant functions. In this study, we combine the algorithm of data envelopment analysis (DEA) with classification information, and propose a novel DEA-based classifier to construct a piecewise-linear discriminant function, in this classifier, the nonnegative conditions of DEA model are loosed and class information is added; Finally, experiments are performed using a UCI data set to demonstrate the accuracy and efficiency of the proposed model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, T. W. (1984). An introduction to multivariate statistical analysis. New York: Wiley.
Bajgier, S. M., & Hill, A. V. (1982). An experimental comparison of statistical and linear programming approaches to the discriminant problem. Decision Sciences, 13, 604–618.
Bal, H., & Orkcu, H. H. (2007). Data envelopment analysis approach to two-group classification problem and experimental comparison with some classification models. Hacettepe Journal of Mathematics and Statistics, 36(2), 169–180.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.
Bennett & Mangasarian. (1992). http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Original%29.
Bo, Z., Benhui, C., & Jinglu, H. U. (2014). Quasi-linear support vector machine for nonlinear classification. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E, 97(A7), 1587–1594.
Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data and Knowledge Discovery, 2(2), 121–167.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Chen, X., Yang, J., Zhang, D., & Liang, J. (2013). Complete large margin linear discriminant analysis using mathematical programming approach. Pattern Recognition, 46, 1579–1594.
Cohen, S., Robach, L., & Maimon, O. (2007). Decision-tree in stance-space decomposition with groped gain-ratio. Information Sciences, 177, 3557–3573.
Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188.
Fred, N., & Glover, F. (1981). A linear programming approach to the discriminant problem. Decision Sciences, 12, 68–74.
Fred, N., & Glover, F. (1986). Evaluating alternative linear programming models to solve the two-group discriminant problem. Decision Sciences, 17, 589–585.
Glen, J. J. (2005). Mathematical programming models for piecewise-linear discriminant analysis. Journal of the Operational Research Society, 56, 331–341.
Han, J., & Kamber, M. (2001). Data mining: Concepts and techniques. San Francisco: Morgan Kaufman Publishers Inc.
Lam, K. F., Choo, E. U., & Moy, J. W. (1996). 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.
Lam, K. F., & Moy, J. W. (2002). Combining discriminant methods in solving classification problems in two-group discriminant analysis. European Journal of Operational Research, 138, 294–301.
Lu, H., Rudy, S., & Liu, H. (1996). Effect data mining using neural networks. IEEE Transaction on Knowledge and Data Engineering, 8(6), 957–961.
Masoumzadeh, A., Toloo, M., & Amirteimoori, A. (2016). Performance, assessment in production systems without explicit inputs: An application to basketball players. IMA Journal of Management Mathematics, 27, 143–156.
Peng, L. Z., Yang, B., Cheng, Y., & Abraham, A. (2009). Data gravitation based classification. Information Sciences, 179, 809–819.
Toloo, M. (2013). The most efficient unit without explicit inputs: An extended MILP-DEA model. Measurement, 46, 3628–3634.
Toloo, M., & Jalili, R. (2016). LU decomposition in DEA with an application to hospitals. Computational Economics, 47(3), 473–488.
Toloo, M., & Kresta, A. (2014). Finding the best asset financing alternative: A DEA-WEO approach. Measurement, 55, 288–294.
Toloo, M., Masoumzadeh, A., & Barat, M. (2015). Finding an initial basic feasible solution for DEA models with an application on bank industry. Computational Economics, 45(2), 323–326.
Toloo, M., Saen, R. F., & Azadi, M. (2015). Obviating some of the theoretical barriers of data envelopment analysis discriminant analysis (DEA-DA): An application in predicting cluster membership of customers. Journal of the Operational Research Society, 66, 674–683.
Troutt, M. D., Rai, A., & Zhang, A. (1996). The potential use of DEA for credit applicant acceptance systems. Computers and Operations Research, 23(4), 405–408.
Vapnik, V. N. (1995). The nature of statistical learning theory. Berlin: Springer.
Wei, Q., Chang, T.-S., & Han, S. (2014). Quantile-DEA classifiers with interval data. Annals of Operations Research, 217, 535–563.
Yan, H., & Wei, Q. (2011). Data envelopment analysis classification machine. Information Sciences, 181, 5029–5041.
Yi, W. G., Lu, M. Y., & Liu, Z. (2011). Multi-valued attribute and multi-labeled data decision tree algorithm. International Journal of Machine Learning and Cybernetics, 2(2), 67–74.
Acknowledgements
This work was supported by a grant from National Social Science Fund of China (14BJY010), National Natural Science Foundation of China (41201327), science and technology research and development programs of Hebei Province (12276104D-3) and Research Foundation of Medicine in Hebei University (2012A3003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ji, Ab., Ji, Y. & Qiao, Y. DEA-Based Piecewise Linear Discriminant Analysis. Comput Econ 51, 809–820 (2018). https://doi.org/10.1007/s10614-016-9642-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10614-016-9642-8