加权稳健支撑向量回归方法

给出一类基于奇异值软剔除的加权稳健支撑向量回归方法(WRSVR)．该方法的基本思想是首先由支撑向量回归方法(SVR)得到一个近似支撑向量回归函数，基于这个近似模型给出了加权SVR目标函数并利用高效的SVR求解技巧得到一个新的近似模型，然后再利用这个新的近似模型重新给出一个加权SVR目标函数并求解得到一个更为精确的近似模型，重复这一过程直至收敛．加权的目的是为了对奇异值进行软剔除．该方法具有思路简捷、稳健性强、容易实现等优点．实验表明，新算法WRSVR比标准SVR方法、稳健支撑向量网(RSVR)方法和加权最小二乘支撑向量机方法(WLS—SVM)更加稳健，算法的逼近精度受奇异值的影响远小于SVM、RSVR和WLS—SVM算法．

Reweighted Robust Support Vector Regression Method

A reweighted robust support vector machine (WRSVR) is presented for regression estimation and function approximation by soft pruning of outliers. The essential idea of the approach is to reweight regularization parameters to softly prune the outliers. Fundamentally, the regression function is improved iteratively. First, an approximate regression function is obtained using support vector regression (SVR), and then a weighted SVR objective function is generated and a new approximate regression function is got by solving the corresponding minimization problem. Based on the new approximate regression function, another weighted SVR objective function is found and a new approximate regression function is obtained. This procedure is repeated until it converges. The new approach is conceptually simple, insensitive to outliers and easy to implement. Numerical simulations show that it is more robust than the currently used Standard SVR, Robust Support Vector Regression Networks and Weighted Least Square SVM.