模糊最小包含球支持向量机
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摘要
为提高支持向量机的模式分类性能,综合模糊支持向量机和球形支持向量机等方法,提出一种模糊最小包含球(FMEB)支持向量机,对于模式分类问题,通过引入模糊隶属度,寻找2个分别包含二类模式的同心最小包含球,使类间间隔最大化,同时二类模式类内分布最小化,从而增强泛化性和鲁棒性。实验结果证明FMEB的模式分类性能优于其他方法。
In order to improve the classification performance of hypersphere Support Vector Machine(SVM),this paper proposes Fuzzy Minimum Enclosing Ball(FMEB) SVM by integrating several state-of-art classification methods such as Fuzzy Support Vector Machine(FSVM) and Hypersphere Support Vector Machine(HSVM).For pattern classification problem,the basic idea of FMEB is to find two optimal minimum enclosing hyperspheres by introducing fuzzy membership,so that each binary class is enclosed by them respectively,and the margin between one class pattern and the enclosing hypersphere is maximized,thus improving the generalization performance and robustness of hypersphere SVM.Experimental results prove that FMEB is more effective than other methods.
In order to improve the classification performance of hypersphere Support Vector Machine(SVM),this paper proposes Fuzzy Minimum Enclosing Ball(FMEB) SVM by integrating several state-of-art classification methods such as Fuzzy Support Vector Machine(FSVM) and Hypersphere Support Vector Machine(HSVM).For pattern classification problem,the basic idea of FMEB is to find two optimal minimum enclosing hyperspheres by introducing fuzzy membership,so that each binary class is enclosed by them respectively,and the margin between one class pattern and the enclosing hypersphere is maximized,thus improving the generalization performance and robustness of hypersphere SVM.Experimental results prove that FMEB is more effective than other methods.
引文
[1]陶剑文,王士同.具有磁场效应的大间隔支持向量机[J].电子与信息学报,2011,33(5):1055-1061.
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[6]Hao Peiyi,Chiang J H.A New Maximal Margin SphericalStructured Multi-class Support Vector Machine[J].AppliedIntelligence,2009,30(2):98-111.
[7]Lin Chunfu,Wang Shengde.Fuzzy Support VectorMachines[J].IEEE Trans.on Neural Network,2002,13(2):464-471.
[8]吴定海,张培林.基于支持向量的单类分类方法综述[J].计算机工程,2011,37(5):187-189.
[9]Müller K R,Mika S,Ratsch G.,et al.An Introduction toKernel-based Learning Algorithms[J].IEEE Trans.onNeural Networks,2001,12(2):181-201.
[10]Sch lkopf B,Smola A J,Williamson R,et al.New SupportVector Algorithms[J].Neural Computation,2000,12(5):1207-1245.
[11]Liu Yi,Zheng Yungfu.Maximum Enclosing and MaximumExcluding Machine for Pattern Description and Discrimi-nation[C]//Proceedings of ICPR’06.Hong Kong,China:IEEE Computer Society Press,2006:129-132.
[12]Wu Mingrui,Ye Jieping.A Small Sphere and Large MarginApproach for Novelty Detection Using Training Data withOutliers[J].IEEE Trans.on Pattern Analysis and MachineIntelligence,2009,31(11):2088-2092.
[2]Vapnik V.The Nature of Statistical Learning Theory[M].[S.l.]:Springer-Verlag,1995.
[3]Tax D M J,Duin R P W.Support Vector Data Descrip-tion[J].Machine Learning,2004,54(1):45-66.
[4]文传军,詹永照.最大间隔最小体积球形支持向量机[J].控制与决策,2010,25(1):79-83.
[5]Wang Jigang,Neskovic P,Cooper L N.Pattern Classifi-cation via Single Sphere[J].Lecture Notes in ComputerScience,2005,37(5):241-252.
[6]Hao Peiyi,Chiang J H.A New Maximal Margin SphericalStructured Multi-class Support Vector Machine[J].AppliedIntelligence,2009,30(2):98-111.
[7]Lin Chunfu,Wang Shengde.Fuzzy Support VectorMachines[J].IEEE Trans.on Neural Network,2002,13(2):464-471.
[8]吴定海,张培林.基于支持向量的单类分类方法综述[J].计算机工程,2011,37(5):187-189.
[9]Müller K R,Mika S,Ratsch G.,et al.An Introduction toKernel-based Learning Algorithms[J].IEEE Trans.onNeural Networks,2001,12(2):181-201.
[10]Sch lkopf B,Smola A J,Williamson R,et al.New SupportVector Algorithms[J].Neural Computation,2000,12(5):1207-1245.
[11]Liu Yi,Zheng Yungfu.Maximum Enclosing and MaximumExcluding Machine for Pattern Description and Discrimi-nation[C]//Proceedings of ICPR’06.Hong Kong,China:IEEE Computer Society Press,2006:129-132.
[12]Wu Mingrui,Ye Jieping.A Small Sphere and Large MarginApproach for Novelty Detection Using Training Data withOutliers[J].IEEE Trans.on Pattern Analysis and MachineIntelligence,2009,31(11):2088-2092.