A bilateral-truncated-loss based robust support vector machine for classification problems

Support vector machine (SVM) is sensitive to outliers or noise in the training dataset. Fuzzy SVM (FSVM) and the bilateral-weighted FSVM (BW-FSVM) can partly overcome this shortcoming by assigning different fuzzy membership degrees to different training samples. However, it is a difficult task to set the fuzzy membership degrees of the training samples. To avoid setting fuzzy membership degrees, from the beginning of the BW-FSVM model, this paper outlines the construction of a bilateral-truncated-loss based robust SVM (BTL-RSVM) model for classification problems with noise. Based on its equivalent model, we theoretically analyze the reason why the robustness of BTL-RSVM is higher than that of SVM and BW-FSVM. To solve the proposed BTL-RSVM model, we propose an iterative algorithm based on the concave–convex procedure and the Newton–Armijo algorithm. A set of experiments is conducted on ten real world benchmark datasets to test the robustness of BTL-RSVM. The statistical tests of the experimental results indicate that compared with SVM, FSVM and BW-FSVM, the proposed BTL-RSVM can significantly reduce the effects of noise and provide superior robustness.