Capped L2,p-Norm Metric Based on Robust Twin Support Vector Machine with Welsch Loss
Haoyu Wang, Guolin Yu, Jun Ma
Abstract
A twin bounded support vector machine (TBSVM) is a phenomenon of symmetry that improves the performance of the traditional support vector machine classification algorithm. In this paper, we propose an improved model based on a TBSVM, called a Welsch loss with capped L2,p-norm distance metric robust twin bounded support vector machine (WCTBSVM). On the one hand, by introducing the capped L2,p-norm metric in the TBSVM, the problem of the non-sparse output of the regularization term is solved; thus, the generalization and robustness of the TBSVM is improved and the principle of minimizing the structural risk is realized. On the other hand, a bounded, smooth, and non-convex Welsch loss function is introduced to reduce the influence of noise, which further improves the classification performance of the TBSVM. We use a half-quadratic programming algorithm to solve the model non-convexity problem caused by Welsch loss. Therefore, the WCTBSVM is more robust and effective in dealing with noise compared to the TBSVM. In addition, to reduce the time complexity and speed up the convergence of the algorithm, we constructed a least squares version of the WCTBSVM, named the fast WCTBSVM (FWCTBSVM). Experimental results on both UCI and artificial datasets show that our model can show better classification performance on classification problems.