基于线性距离核的支持向量机设计
|
摘要
为了消除样本数量对现有SVM决策函数计算的影响,提出一种基于样本数据线性距离特征的线性距离核函数来改进SVM。基于该核函数的SVM决策函数,实现了与样本数量无关的分类计算,极大提升SVM在执行超大规模分类计算的速度。仿真结果表明,该核函数具有与常用核函数一样的性能,可以完成非线性SVM的训练和分类。
In order to solve the impact of sample number in support vector machines(SVM)decision function,the linear distance kernel function(LDF)is proposed based on distance characteristics of the sample data to improve the SVM decision function.Existing non-linear kernel in SVM decision function may need massive support vector to participate caculation,especially when the SVM training result is far from target.As a result of the surface structure is too complex to increase greatly the number of support vectors,a novel kernel function for SVM is proposed that consists of linear distance metric method,achieving the aim of the decision function regardless of sample number which implements classification without support vectors.Mathematical simulation results show that the training and classification of the SVM improved by our kernel function can be performed.
In order to solve the impact of sample number in support vector machines(SVM)decision function,the linear distance kernel function(LDF)is proposed based on distance characteristics of the sample data to improve the SVM decision function.Existing non-linear kernel in SVM decision function may need massive support vector to participate caculation,especially when the SVM training result is far from target.As a result of the surface structure is too complex to increase greatly the number of support vectors,a novel kernel function for SVM is proposed that consists of linear distance metric method,achieving the aim of the decision function regardless of sample number which implements classification without support vectors.Mathematical simulation results show that the training and classification of the SVM improved by our kernel function can be performed.
引文
[1]Bradford B C.The quickhull algorithm for convex hulls[J].ACM Transactions on Mathematical Software,1996,22(4):469-483.
[2]Platt J C.Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines[M].[S.l.]:Microsoft Research,1998.
[3]Keerthi S S Shevade S K,Bhattacharyya C,et al.Improvements to Platt′s SMO algorithm for SVM classifier design[J].Neural Computation,2001,13(3):637-649.
[4]Chapelle O,Haffner P,Vapnik V N.Support vector machines for histogram-based image classification[J].IEEE Transactions on Neural Networks,1999,10(5):1055-1064.
[5]Amari S,Wu S.Improving support vector machine classifiers by modifying kernel functions[J].Neural Networks,1999,12(6):783-789.
[6]Zhang Xuegong.Pattern Recognition[M].Third Edition.Beijing:Tsinghua University Press,2010.
[7]Cristianini N,John S T.An Introduction to Support Vector Machines and Other Kernel-based Learning Methods[M].Beijing:Electronics Industry Press,2004.
[8]USPS Handwritten Digits(test and train data set)[EB/OL].[2013-05-20].http://www.datatang.com/data/12087.
[9]MIT-CBCL face recognition database[EB/OL].[2013-05-10].http://cbcl.mit.edu/software-datasets/heisele/facerecognition-database.html.
[2]Platt J C.Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines[M].[S.l.]:Microsoft Research,1998.
[3]Keerthi S S Shevade S K,Bhattacharyya C,et al.Improvements to Platt′s SMO algorithm for SVM classifier design[J].Neural Computation,2001,13(3):637-649.
[4]Chapelle O,Haffner P,Vapnik V N.Support vector machines for histogram-based image classification[J].IEEE Transactions on Neural Networks,1999,10(5):1055-1064.
[5]Amari S,Wu S.Improving support vector machine classifiers by modifying kernel functions[J].Neural Networks,1999,12(6):783-789.
[6]Zhang Xuegong.Pattern Recognition[M].Third Edition.Beijing:Tsinghua University Press,2010.
[7]Cristianini N,John S T.An Introduction to Support Vector Machines and Other Kernel-based Learning Methods[M].Beijing:Electronics Industry Press,2004.
[8]USPS Handwritten Digits(test and train data set)[EB/OL].[2013-05-20].http://www.datatang.com/data/12087.
[9]MIT-CBCL face recognition database[EB/OL].[2013-05-10].http://cbcl.mit.edu/software-datasets/heisele/facerecognition-database.html.