Abstract
Support Vector Machine is a kind of algorithm used for classifying linear and nonlinear data, which not only has a solid theoretical foundation, but is more accurate than other sorting algorithms in many areas of applications, especially in dealing with high-dimensional data. It is not necessary for us to get the specific mapping function in solving quadratic optimization problem of SVM, and the only thing we need to do is to use kernel function to replace the complicated calculation of the dot product of the data set, reducing the number of dimension calculation. This paper introduces the theoretical basis of support vector machine, summarizes the research status and analyses the research direction and development prospects of kernel function.
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References
Boser B, Guyon I, Vapnik V (1992) A training algorithm for optimal margin classifiers [C]. In: Proceedings of the 5th annual ACM conference on computational learning theory, Pittsburgh, pp 144–152
Vapnik VN (2000) The nature of statistical learning theory [M]. Translated by Zhang Xuegong (trans: Zhang X). Tsinghua University Press, Beijing
Vapnik VN (2004) Statistical learning theory [M]. Translated by Xu Jianhua, Zhang Xuegong (trans: Xu J, Zhang X). Publishing House of Electronics Industry, Beijing
Vapnik V (1995) The nature of statistical learning theory [M]. Springer, New York
Ju C, Guo F (2010) A distributed data mining model based on support vector machines DSVM [J]. 30(10):1855–1863
Zhu S, Zhang R (2008) Research for selection of kernel function used in support vector machine [J]. Sci Technol Eng 8(16):4513–4517
Cristianini, N, Taylor Shawe J, Kandola J et al. (2002) On kernel target alignment. In: Proceedings neural information processing systems. MIT Press, Cambridge, pp 367–373
Yang Z (2008) Kernel-based support vector machines [J]. Comput Eng Appl 44(33):1–6
Li T, Wang X (2013) A semi-supervised support vector machine classification method based on cluster kernel [J]. Appl Res Comput 30(1):42–45
Tison C, Nicolas JM, Tupin F et al. (2004) A new statistical model for Markovian classification of urban areas in high-resolution SAR images [J]. IEEE Trans Geosci Remote Sens 42(10):2046–2057
Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York
Wu Z, Gao X, Xie W (2004) A study of a new fuzzy clustering algorithm based on the kernel method. Journal of Xi ‘an university of electronic science and technology magazine, 31(4):533–537
Zhang N, Zhang Y (2010) Support vector machine ensemble model based on KFCM and its application [J]. J Comput Appl 30(1):175–177
Cao W, Zhao Y, Gao S (2010) Multi-class support vector machine based on fuzzy kernel clustering [J]. CIESC Journal 61(2):420–424
Angulo C, Parra X (2003) K-SVCR Andreu Catala. A support vector machine for multi-class classification [J]. Neurocomputing 55(9):55–77
Platt JC, Cristianini N, Shawe-Taylor J (2000) Large margin DAGs for multiclass classification [J]. Adv Neural Inf Proc Syst 12(3):547–553
Zhao H, Rong L (2006) SVM multi-class classification based on fuzzy kernel clustering [J]. Syst Eng Electron 28(5):770–774
Yang Z (2008) Research progress of the kernel function support vector machine [J]. Sci Technol Inf 19:209–210
Jia L, Liao S (2008) Support vector machines with hyper-kernel functions [J]. Comput Sci 35(12):148–150
Guo L, Sun S, Duan X (2008) Research for support vector machine and kernel function [J]. Sci Technol Eng 8(2):487–489
Collobert R, Bengio S (2001) SVM torch: support vector machines for large-scale regression problems. J Mach Learn Res 1:143–160
Cheng SO, Smola AJ, Williamson RC (2005) Learning the kernel with hyper-kernel. J Mach Learn Res 6:1043–1071
Platt J, Burges CJC (1998) Fast training of support vector machines sequential minimal optimization. In: Sholkpof B, Smola AJ (eds) MIT Press, Cambridge
Tao W (2003) Kernels’ properties, tricks and its application on obstacle detection [J]. National University of Defense Technology, Changsha
Y Fu, D Ren (2010) Kernel function and its parameters selection of support vector machines [J]. Sci Technol Innov Herald 9:6–7
Chapelle O, Vapnik V, Bousquet O et al (2002) Choosing multiple parameters for support vector machines [J]. Mach Learn 46(1):131–159
Men C, Wang W (2006) Kernel parameter selection method based on estimation of convex [J]. Comput Eng Des 27(11):1961–1963
Qi Z, Tian Y, Xu Z (2005) Kernel-parameter selection problem in support vector machine [J]. Control Eng China 12(44):379–381
Chen PW, Wang JY, Lee HM (2004) Mode selection of SVNs using GA approach [C]. Proceedings of 2004 IEEE international joint conference on neural networks. IEEE Press, Piscataway, pp 2035–2040
Zheng CH et al. (2004) Automatic parameters selection for SVM based on GA [C]. Proceedings of the 5th World congress on intelligent control and automation, IEEE Press, Piscataway, pp 1869–1872
Liu X, Luo B, Qian Z (2005) Optimal model selection for support vector machines [J]. J Comput Res Dev 42(4):576–581
Wang T, Chen J (2012) Survey of research on kernel selection [J]. Comput Eng Des 33(3):1181–1186
Acknowledgments
This work has been supported by the National Natural Science Foundation of China under Grant 61172072, 61271308, and Beijing Natural Science Foundation under Grant 4112045, and the Research Fund for the Doctoral Program of Higher Education of China under Grant W11C100030, the Beijing Science and Technology Program under Grant Z121100000312024.
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Liu, L., Shen, B., Wang, X. (2014). Research on Kernel Function of Support Vector Machine. In: Huang, YM., Chao, HC., Deng, DJ., Park, J. (eds) Advanced Technologies, Embedded and Multimedia for Human-centric Computing. Lecture Notes in Electrical Engineering, vol 260. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7262-5_93
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DOI: https://doi.org/10.1007/978-94-007-7262-5_93
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