Optimization model and application of linear and nonlinear MBSVM based on pinball loss function

The multiple birth support vector machine (MBSVM) typically utilizes a hinge loss function, which is susceptible to noise sensitivity and instability during resampling. To overcome these issues, we introduce two models: linear and nonlinear MBSVM models, both utilizing a pinball loss function. The main goal of these models is to improve the classification performance and noise resilience of the Pin-MBSVM by optimizing the maximum quantile distance. Additionally, to decrease the computation time for these models, we provide an in-depth discussion of a fast algorithm based on the successive overrelaxation (SOR) iteration method. In experiments, we test the Pin-MBSVM algorithm using both UCI datasets and synthetic datasets, comparing its performance with OVO-TWSVM, OVA-TWSVM and MBSVM. The results show that our methods successfully reduce the noise sensitivity and resampling instability found in traditional MBSVM while preserving the model’s computational efficiency. Finally, the effectiveness of our model was validated using the Friedman test and Bonferroni–Dunn test.