Robust Least Square Support Vector Regression for Contaminated Data Modeling

Weighted least squares support vector machine (WLSSVM) is a robust version of least squares support vector machine (LS-SVM). It adds weights on error variables to eliminate the influence of outliers. But the weights, which largely depend on the original regression errors from unweighted LS-SVM, might be unreliable for correcting the biased estimation of LS-SVM, especially for the training data set with large deviation outliers. In this paper, a twostage weighting strategy is proposed. This approach derives from the idea of spatial rank of feature vector, and down-weights these large deviation outliers firstly. Then the weights are updated by these regression errors of WLSSVM with the weights obtained in the first weighting stage. Finally, WLS-SVM is again employed to further improve the prediction performance. The effectiveness of the proposed robust LS-SVM is validated by two artificial data examples and a soft sensor modeling problem.