Support vector regression with the weighted absolute deviation error loss function

Abstract

In this paper we propose robust support vector regression algorithms to deal with noisy data sets. We adopt the absolute deviation error function for a loss function of regression model, and the proposed algorithms preserves the structure of the least squares support vector regression. The proposed algorithms are very fast and the procedures are much simpler than other support vector machine algorithms. They are robust to regression outliers, because the loss functions are less increasing than the squares error function for large errors and it uses a weight function for each observation. By comparing the proposed algorithms with other methods for the simulated datasets and benchmark datasets, the proposed methods are more robust than the least squares support vector regression when outliers exist.