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.%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.
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