|本期目录/Table of Contents|

[1]罗林开,叶凌君,周绮凤.常用核函数的几何度量与几何性质[J].厦门大学学报(自然科学版),2009,48(06):804.
 LUO Lin kai,YE Ling jun,ZHOU Qi feng.Geometric Measures and Properties of Commonly Used Kernel Functions[J].Journal of Xiamen University(Natural Science),2009,48(06):804.
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
48卷
期数:
2009年06期
页码:
804
栏目:
研究论文
出版日期:
2009-11-20

文章信息/Info

Title:
Geometric Measures and Properties of Commonly Used Kernel Functions
作者:
罗林开叶凌君周绮凤
厦门大学信息科学与技术学院,福建 厦门 361005
Author(s):
LUO LinkaiYE LingjunZHOU Qifeng
School of Information Science and Technology,Xiamen University,Xiamen 361005,China
关键词:
支持向量机核选择几何度量几何性质
Keywords:
SVMkernel function selectiongeometric measuregeometric property
分类号:
TP 181
文献标志码:
-
摘要:
研究核函数的几何度量和几何性质,并给出核函数选择(核选择)的建议.首先通过对核函数所蕴含的几何度量的深入分析,导出了常用的高斯径向基核函数和多项式核函数的黎曼度量、距离度量和角度度量;然后总结了这些几何度量的性质,并进行了数学证明;最后在几何性质的基础上,给出了核选择的一些建议.
Abstract:
The geometric measures and properties of the kernel functions were studied and some suggestions about the selection of kernel functions were presented.By deeply analyzing the geometric measures of the kernel functions,the Riemann measures,distance measures and angle measures of the commonly used Gaussian radial basis kernel function and polynomial kernel function were deduced at first.Then the properties of these geometric measures were summarized and the mathematical proofs were finished.Finally some suggestions about selection of kernel functions based on the geometric properties were given.

参考文献/References:


[1]Vapnik V N.Statistical learning theory[M].New York: Wiley,1998.
[2]Burges C.A tutorial on support vector machines for pattern recognition[J].Data Mining and Knowledge Discovery,1998,2(2):121-167.
[3]邓乃扬,田英杰.数据挖掘中的新方法——支持向量机[M].北京:科学出版社,2004.
[4]LiJ,Allinson N,Tao D C,et al.Multitraining supportvector machine for image retrieval[J].IEEE Transactions on Image Processing,2006,15(11):3597-3601.
[5]Graf A B A,Wichmann F A,Bülthoff H H,et al.Classification of faces in man and machine[J].Neural Computation,2006,18(1):143-165.
[6]Luo L K,Peng H,Zhang Q S,et al.A comparison ofstrategies for unbalance sample distribution in support vector machine[C]//Proceeding of 1st IEEE Conference on Industrial Electronics and Applications.Singapore:IEEE Press,2006:128-132.
[7]张秋水,罗林开,刘晋闽.基于支持向量机的中国上市公司财务困境预测[J].计算机应用,2006,26(Sup.): 105-107.
[8]Chapelle O,Vapnik V,Bousquet O,et al.Choosing multiple parameters for support vector machines[J].Machine Learning,2002,46(1):131-159.
[9]Cristianini N,ShaweTaylor J,Elisseeff A,et al.On kerneltarget alignment[J].Advances in Neural Information Processing Systems,2002,14:367-373.
[10]Lanckriet G R G,Cristianini N,Bartlett P,et al.Learning the kernel matrix with semidefinite programming[J].Journal of Machine Learning Research,2004,5:27-72.
[11]Amari S,Wu S.Improving support vector machine classifiers by modifying kernel functions[J].Neural Networks,1999,12(6):783-789.
[12]Burges C J C.Geometry and invariance in kernel based methods,advances in kernel methods: support vector learning[M].Cambridge,Mass:MIT Press,1999.
[13]Wu G,Chang E Y.KBA:kernel boundary alignmentconsidering imbalanced data distribution[J].IEEE Transactions on Knowledge and Data Engineering,2005,17(6): 786-795.

备注/Memo

备注/Memo:
收稿日期:20090410 基金项目:福建省自然科学基金(2008J0033)资助 Email:luolk@xmu.edu.cn
更新日期/Last Update: 2012-09-05