A kernel-free quadratic surface twin support vector machine with capped L1-norm distance metric for robust classification

Qi Si, Zhixia Yang, Jinbiao Zhao, Rongda Chen

Abstract: Highlights•This paper proposes CL1<math><msub is="true"><mrow is="true"><mi is="true">L</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math>QTSVM by integrating kernel-free technique and capped L1<math><msub is="true"><mrow is="true"><mi is="true">L</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math>-norm distance metric.•The introduction of the L2<math><msub is="true"><mrow is="true"><mi is="true">L</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> regularization term enhances the generalization of the model.•A efficient iterative algorithm is designed using re-weighting techniques and the Sherman–Morrison–Woodbury theorem.•Theoretical analysis covers algorithm convergence, time complexity, and the existence of locally optimal solutions to the non-smooth primal optimization problem.•Numerical experiments on multiple datasets validate the classification performance and robustness of the proposed model.