Robust kernel-free double well potential twin support vector regression

Twin support vector regression (TSVR) has demonstrated superior computational efficiency compared with SVR and has been extensively applied across various fields. However, the performance of TSVR could be significantly deteriorated by outliers because of the utilization of the L2 norm loss function. We propose a robust kernel-free quartic surface TSVR model to address this issue by utilizing a novel robust loss function and the double well potential (DWP) function. The proposed robust loss function combines the L1 and L2 norm loss functions through a hyperparameter designed to be robust against outliers. The proposed double well potential TSVR (DWPTSVR) extends the application of the kernel-free DWP function in TSVR for the first time. Unlike conventional kernel methods that require time-consuming kernel parameter searching, the proposed DWPTSVR model eliminates this step by predefining a nonlinear surface. Extensive experimental results indicate that the proposed DWPTSVR outperforms previous well-established kernel-based or kernel-free SVR and TSVR models in terms of accuracy and robustness on ten artificial datasets and eight benchmark datasets with different types of outliers. The sensitivity analysis results reveal that the proposed DWPTSVR model with the combination of L1 and L2 norm loss functions performs significantly better than the model with L1 or L2 norm loss functions. Moreover, the proposed DWPTSVR model is validated to be successfully applied in two time series datasets and three large-scale real-world datasets. In addition, an efficient version of DWPTSVR is also developed to deal with large-scale high-dimensional datasets.