A Novel Twin Support-Vector Machine With Pinball Loss

Twin support-vector machine (TSVM), which generates two nonparallel hyperplanes by solving a pair of smaller-sized quadratic programming problems (QPPs) instead of a single larger-sized QPP, works faster than the standard SVM, especially for the large-scale data sets. However, the traditional TSVM adopts hinge loss which easily leads to its sensitivity of the noise and instability for resampling. To enhance the performance of the TSVM, we present a novel TSVM with the pinball loss (Pin-TSVM) which deals with the quantile distance and is less sensitive to noise points. We further investigate its properties, including the noise insensitivity, between-class distance maximization, and within-class scatter minimization. In addition, we compare our Pin-TSVM with the twin parametric-margin SVM and the SVM with the pinball loss in theory. Numerical experiments on a synthetic data set and 14 benchmark data sets with different noises demonstrate the feasibility and validity of our proposed method.