LS-SVM稳健设计及正则化性能分析

A Robust Design of LS-SVM and Analysis of Regularization Performance

LS-SVM(最小二乘支持向量机)把传统的支持向量机求解由二次规划变为求解线性方程组问题,使得在计算效率和算法设计的简单性上都有很大提高。然而,LS-SVM由于其误差函数是二次函数,对训练样本中的野值比较敏感,采用传统的LS-SVM方法,容易歪曲系统,并可能直接导致函数逼近失败。针对这一情况,基于最优化理论及稳健估计思想,提出了RLS-SVM(稳健LS-SVM)的设计方法。数值计算表明,在有野值的情况下,RLS-SVM对函数逼近具有良好的稳健性。另外,分析了正则化因子与核函数的选择对逼近性能的影响,并给出了在不同情况下的一些使用规则。

LS-SVM（Least Square Support Vector Machine） has received much attention in recent years due to its efficient and convenient algorithms that switch training process by solving a set of linear equations rather than a quadratic programming problem.However,LS-SVM regressors are not robust to outliers because of the square error function.A design of Robust LS-SVM（RLS-SVM） is proposed in this paper with a description of the algorithm that provides a solution to the problem.Numerical computation results indicate that RLS-SVM exerts robust performance in presence of outliers in training data.Regularization factors and kernel functions on approximation performance are also analyzed and rules on how to make choices are given.