A robust weighted least squares support vector regression based on least trimmed squares

highlights
• A robust weighted LSSVM was presented.
• LTS-based LSSVM with C-steps was used to obtain robust results.
• A reweighted LSSVM was adopted to improve efficiency.
• The new estimator was validated with two groups of examples.

In order to improve the robustness of the classcial LSSVM when dealing with sample points in the presence of outliers, we have developed a robust weighted LSSVM (reweighted LSSVM) based on the least trimmed squares technique (LTS). The procedure of the reweighted LSSVM includes two stages, respectively used to increase the robustness and statistical efficiency of the estimator. In the first stage, LTS-based LSSVM (LSSVM-LTS) with C-steps was adopted to obtain robust simulation results at the cost of losing statistical efficiency to some extent. Thus, in the second stage, the results computed in the first stage were optimized with a weighted LSSVM to improve efficiency. Two groups of examples including numerical tests and real-world benchmark examples were respectively employed to compare the robustness of the reweighted LSSVM with those of the classical LSSVM, the weighted LSSVM and LSSVM-LTS. Numerical tests indicate that the reweighted LSSVM is comparable to the weighted LSSVM, and more accurate than the classical LSSVM and LSSVM-LTS when the contaminating proportion is small (i.e. 0.1 and 0.2), whereas with the increase of contaminating proportion, the reweighted LSSVM performs much better than other methods. The real-world exmaple of regressing seven benchmark datasets demonstrates that the reweighted LSSVM is always more accurate than other versions of LSSVM. In conclusion, the newly developed method can be considered as an alternative to function estimation, especially for sample points in the presence of outliers.