Computer Engineering and Applications ›› 2008, Vol. 44 ›› Issue (2): 70-73.

• 学术探讨 • Previous Articles     Next Articles

Approximately linear dependency between r and input noise in r-Support Vector Regression

ZHOU Xiao-jian,ZHU Jia-gang,WANG Shi-tong   

  1. School of Information Engineering,Jiangnan University,Wuxi,Jiangsu 214122,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2008-01-11 Published:2008-01-11
  • Contact: ZHOU Xiao-jian

R-SVR中r与输入噪声间近似线性反比关系

周晓剑,朱嘉钢,王士同   

  1. 江南大学 信息工程学院,江苏 无锡 214122
  • 通讯作者: 周晓剑

Abstract: The dependency relationship between r and the input noise in r-SVR is studied using SVR Bayesian evidence framework.First,focus is paid on the cases of laplacian noise and uniform noise,and the approximately inversely linear dependencies between r and the variances of the two noises are then respectively derived.Second,with the relevant conclusion on r-SVR and experimental study,the more general claim is then proposed that the approximately inversely linear dependency is almost kept between r and the input noise in r-SVR.Such a dependency relationship is useful to determine the optimal choice for r in Norm-r loss function in the existence of unknown input noise.

Key words: Support Vector Machines(SVM), Support Vector Regression(SVR), Norm-r function

摘要: 为使r范数SVR更具鲁棒性,深入研究了r范数SVR中参数与输入噪声之间的关系。运用SVR的贝叶斯框架,分别推导出了鲁棒的r范数SVR中参数r与拉斯噪声和均匀噪声之间呈近似的线性反比关系。并结合仿真结果和已有的相关结论,得到了更为一般的结论,即鲁棒的r范数SVR中参数r与输入噪声之间呈近似的线性反比关系。这一结论为输入样本含有分布未知噪声的情况下r范数SVR参数的选择提供了理论依据。

关键词: 支持向量机, 支持向量回归机, r范数损失函数