A New Formulation for Cost-Sensitive Two Group Support Vector Machine with Multiple Error Rate

Document Type : Research Paper


Faculty of Industrial Engineering, K.N.Toosi University of Technology


Support vector machine (SVM) is a popular classification technique which classifies data using a max-margin separator hyperplane. The normal vector and bias of the mentioned hyperplane is determined by solving a quadratic model implies that SVM training confronts by an optimization problem. Among of the extensions of SVM, cost-sensitive scheme refers to a model with multiple costs which considers different error rates for misclassification. The cost-sensitive scheme is useful when misclassifications cannot be considered equal. For example, it is true for medical diagnosis. In such cases, misclassifying a patient as healthy implies more loss in comparison to the opposite loss. Therefore, cost-sensitive scheme poses as a modified model and hereby aims at minimizing loss function instead of generalization error. This paper, concentrates on a new formulation cost-sensitive classification considering both misclassification cost and accuracy measures. Also, in the training phase a new heuristic algorithm will be used to solve the proposed model. The superiority of the novel method is affirmed after comparing to the traditional ones.


Main Subjects

Cao, P., Zhao, D., & Zaiane, O. (2013, April). An optimized cost-sensitive SVM for imbalanced data learning. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 280-292). Springer Berlin Heidelberg.
Chen, X. L., Jiang, Y., Chen, M. J., Yu, Y., Nie, H. P., & Li, M. (2012). A Dynamic Cost Sensitive Support Vector Machine. In Advanced Materials Research (Vol. 424, pp. 1342-1346). Trans Tech Publications.
Chen, Y., & Wang, J. Z. (2003). Support vector learning for fuzzy rule-based classification systems. IEEE Transactions on Fuzzy Systems, 11(6), 716-728.
Crammer, K., & Singer, Y. (2001). On the algorithmic implementation of multiclass kernel-based vector machines. Journal of machine learning research, 2(Dec), 265-292.
Fung, G. M., & Mangasarian, O. L. (2005). Multicategory proximal support vector machine classifiers. Machine learning, 59(1-2), 77-97.
Hwang, J. P., Park, S., & Kim, E. (2011). A new weighted approach to imbalanced data classification problem via support vector machine with quadratic cost function. Expert Systems with Applications, 38(7), 8580-8585.
Mangasarian, O. L., & Musicant, D. R. (2001). Lagrangian support vector machines. Journal of Machine Learning Research, 1(Mar), 161-177.
Mangasarian, O. L., & Wild, E. W. (2001). Proximal support vector machine classifiers. In Proceedings KDD-2001: Knowledge Discovery and Data Mining.
Nedaie, A., & Najafi, A. A. (2016). Polar support vector machine: Single and multiple outputs. Neurocomputing, 171, 118-126.
Platt, J. C., Cristianini, N., & Shawe-Taylor, J. (1999, November). Large Margin DAGs for Multiclass Classification. In nips (Vol. 12, pp. 547-553).
Pontil, M., & Verri, A. (1998). Support vector machines for 3D object recognition. IEEE transactions on pattern analysis and machine intelligence, 20(6), 637-646.
Qi, Z., Tian, Y., & Shi, Y. (2012). Laplacian twin support vector machine for semi-supervised classification. Neural Networks, 35, 46-53.
Qi, Z., Tian, Y., & Shi, Y. (2013). Robust twin support vector machine for pattern classification. Pattern Recognition, 46(1), 305-316.
Shawe-Taylor, J., & Sun, S. (2011). A review of optimization methodologies in support vector machines. Neurocomputing, 74(17), 3609-3618.
Suykens, J. A., De Brabanter, J., Lukas, L., & Vandewalle, J. (2002). Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing, 48(1), 85-105.
Tian, Y., Qi, Z., Ju, X., Shi, Y., & Liu, X. (2014). Nonparallel support vector machines for pattern classification. IEEE transactions on cybernetics, 44(7), 1067-1079.
Tran, Q. A., Li, X., & Duan, H. (2005). Efficient performance estimate for one-class support vector machine. Pattern Recognition Letters, 26(8), 1174-1182.
Turney, P. D. (1995). Cost-sensitive classification: Empirical evaluation of a hybrid genetic decision tree induction algorithm. Journal of artificial intelligence research, 2, 369-409.
Vapnik, V. (1998). Statistical Learning Theory, New York, Wiley.
Wan, J. W., Yang, M., & Chen, Y. J. (2012). Cost sensitive semi-supervised Laplacian support vector machine. Acta Electronica Sinica, 40(7), 1410-1415.
Waring, C. A., & Liu, X. (2005). Face detection using spectral histograms and SVMs. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(3), 467-476.
Yang, C. Y., Wang, J. J., Chou, J. J., & Lian, F. L. (2015). Confirming robustness of fuzzy support vector machine via ξ–α bound. Neurocomputing, 162, 256-266.
Zheng, E. H., Li, P., & Song, Z. H. (2006). Cost sensitive support vector machines. Control and decision, 21(4), 473.
Volume 11, Issue 2
April 2018
Pages 21-30
  • Receive Date: 09 October 2016
  • Revise Date: 29 January 2017
  • Accept Date: 01 August 2018
  • First Publish Date: 01 August 2018