Research on Kernel Function of Support Vector Machine

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.

[1]  Qi Zhi-quan.  Kernel-parameter Selection Problem in Support Vector Machine , 2005 .

[2]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[3]  Rong Li-li.  SVM multi-class classification based on fuzzy kernel clustering , 2006 .

[4]  Zhang Yong-ping.  Support vector machine ensemble model based on KFCM and its application , 2010 .

[5]  Wang Wen-jian.  Kernel parameter selection method based on estimation of convex , 2006 .

[6]  Hahn-Ming Lee,et al.  Model selection of SVMs using GA approach , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[7]  Sayan Mukherjee,et al.  Choosing Multiple Parameters for Support Vector Machines , 2002, Machine Learning.

[8]  WU Zhong-dong.  A study of a new fuzzy clustering algorithm based on the kernel method , 2004 .

[9]  Chen Jun-ting.  Survey of research on kernel selection , 2012 .

[10]  Xu,et al.  Automatic Parameters Selection for SVM Based on PSO , 2007 .

[11]  N. Cristianini,et al.  On Kernel-Target Alignment , 2001, NIPS.

[12]  Henri Maître,et al.  A new statistical model for Markovian classification of urban areas in high-resolution SAR images , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[13]  Yang Zhong-jin.  Kernel-based support vector machines , 2008 .

[14]  Teik-Thye Lim,et al.  Influences of amphiphiles on dechlorination of a trichlorobenzene by nanoscale Pd/Fe: adsorption, reaction kinetics, and interfacial Interactions. , 2008, Environmental science & technology.

[15]  Jiao Licheng,et al.  Automatic parameters selection for SVM based on GA , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[16]  Alexander J. Smola,et al.  Learning the Kernel with Hyperkernels , 2005, J. Mach. Learn. Res..

[17]  Ethem Alpaydin,et al.  Support Vector Machines for Multi-class Classification , 1999, IWANN.

[18]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[19]  Zhang Ren-jie.  Research for Selection of Kernel Functions Used in Support Vector Machine , 2008 .

[20]  Nello Cristianini,et al.  Large Margin DAGs for Multiclass Classification , 1999, NIPS.

[21]  Samy Bengio,et al.  SVMTorch: Support Vector Machines for Large-Scale Regression Problems , 2001, J. Mach. Learn. Res..

[22]  John C. Platt,et al.  Fast training of support vector machines using sequential minimal optimization, advances in kernel methods , 1999 .

[23]  Zhao Yingkai,et al.  Multi-class support vector machines based on fuzzy kernel cluster , 2010 .

[24]  Na Zhang,et al.  Support vector machine ensemble model based on KFCM and its application: Support vector machine ensemble model based on KFCM and its application , 2010 .

[25]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[26]  Luo Bin,et al.  Optimal Model Selection for Support Vector Machines , 2005 .

[27]  E Comak,et al.  A support vector machine using the lazy learning approach for multi-class classification , 2006, Journal of medical engineering & technology.

[28]  Andreu Català,et al.  K-SVCR. A support vector machine for multi-class classification , 2003, Neurocomputing.

[29]  Duan Xiu-sheng.  Research for Support Vector Machine and Kernd Funution , 2008 .

[30]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .