A robust regression based on weighted LSSVM and penalized trimmed squares

Least squares support vector machine (LS-SVM) for nonlinear regression is sensitive to outliers in the field of machine learning. Weighted LS-SVM (WLS-SVM) overcomes this drawback by adding weight to each training sample. However, as the number of outliers increases, the accuracy of WLS-SVM may decrease. In order to improve the robustness of WLS-SVM, a new robust regression method based on WLS-SVM and penalized trimmed squares (WLSSVM–PTS) has been proposed. The algorithm comprises three main stages. The initial parameters are obtained by least trimmed squares at first. Then, the significant outliers are identified and eliminated by the Fast-PTS algorithm. The remaining samples with little outliers are estimated by WLS-SVM at last. The statistical tests of experimental results carried out on numerical datasets and real-world datasets show that the proposed WLSSVM–PTS is significantly robust than LS-SVM, WLS-SVM and LSSVM–LTS.