Abstract
In dealing with the two-class classification problems, the traditional support vector machine (SVM) often cannot achieve good classification accuracy when outliers exist in the training data set. The fuzzy support vector machine (FSVM) can resolve this problem with an appropriate fuzzy membership for each data point. The effect of the outliers can be effectively reduced when the classification problem is solved. In this paper, gray relational analysis (GRA) is employed to search for gray relational grade (GRG) which can be used to describe the relationships between the data attributes and to determine the important samples that significantly influence some defined objectives. A new fuzzy membership function for the FSVM is calculated based on the GRG. This method can distinguish the support vectors and the outliers effectively. Experimental results show that this approach contributes greatly to the reduction of the effect of the outliers and significantly improves the classification accuracy and generalization.
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References
Vapnik VN (1995) The nature of statistical learning theory, vol 2(3). Springer, New York pp 12–19
Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2(2):121–167
Song Q, Hu WJ, Xie WF (2002) Robust support vector machine with bullet hole image classification. IEEE Trans Syst Man Cybern C 32(4):440–448
Lin CF, Wang SD (2002) Fuzzy support vector machines. IEEE Trans Neural Netw 13(2):464–471
Zhang XG (1999) Using class-center vectors to build support vector machines. Proc IEEE Sig Process Soc Workshop 2(2):3–11
Graf ABA, Smola AJ, Borer S (2003) Classification in a normalized feature space using support vector machines. IEEE Trans Neural Networks 14(3):597–605
Jiang XF, Zhang Y, Lv JC (2006) Fuzzy SVM with a new fuzzy membership function. Neural Comput Appl 15(3):268–276
Inoue T, Abe S (2001) Fuzzy support vector machines for pattern classification. In: Proceedings of the IJCNN '01 International Joint Conference on Neural Networks, 1(2):1449–1454
Mercer J (1999) Functions of positive and negative type and their connection with the theory of integral equations. Philos Trans Roy Soc 2(9):415–446
Tosun N (2005) Determination of optimum parameters for multi-performance characteristics in drilling by using grey relational analysis. Int J Adv Manuf Tech 28:450–455
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (Grant No. 10771228), the Natural Science Foundation Project of CQ CSTC (Grant No. CSTC, 2010BB2090), Education Commission project Research Foundation of Chongqing (No. KJ110617, No. 50, No. KJ120628), PR China, and the Program for Innovative Research Team in Higher Educational Institutions of Chongqing, P. R China.
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Tang, W.M., Zhang, Y., Wang, P. (2013). Fuzzy SVM with a New Fuzzy Membership Function Based on Gray Relational Grade. In: Zhong, Z. (eds) Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012. Lecture Notes in Electrical Engineering, vol 216. Springer, London. https://doi.org/10.1007/978-1-4471-4856-2_67
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DOI: https://doi.org/10.1007/978-1-4471-4856-2_67
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