Research On Projection Twin Support Vector Machine Algorithm Based On Different Loss Function

Support Vector Machine(SVM)is a machine learning method based on statistical learning theory and risk minimization principle,which is widely used in many fields.Inspired by SVM,scholars have proposed a variety of non-parallel hyperplane Support Vector Machine algorithms,such as the Projection Twin Support Vector Machine(PTSVM)via within-class variance minimization.Due to its good generalization and classification performance,many scholars have researched PTSVM deeply and put forward various improvement models.In order to improve the computational efficiency and reduce the noise sensitivity and re-sampling instability of PTSVM,two effective improved models have been built.The main research contents of this paper are as follows:(1)Several popular loss functions in classification and regression are analyzed and studied,including 0-1 loss function,Hinge loss function,L1 loss function and Pinball loss function.(2)In order to improve the computational efficiency of PTSVM,a model of PTSVM based on 0-1 loss function(L0-1-PTSVM)is proposed.First,the optimality theory of the model is established,and the relationship between the optimal solution and its proximal stationary point is obtained.Then,alternating direction method of multipliers(ADMM)is used to solve this problem.In order to speed up the iteration of the method,an appropriate working set is selected in each step to reduce the computational complexity.The feasibility and effectiveness of the proposed algorithm are verified on artificial datasets and several UCI benchmark datasets.(3)In order to reduce noise sensitivity and re-sampling instability of PTSVM,an improved Projection Twin Support Vector Machine based on Pinball loss function(Pin-IPTSVM)is proposed in this paper.The linear and nonlinear classification cases of Pin-IPTSVM are obtained,and some properties of the algorithm are analyzed.This algorithm has good generalization performance and can solve the problem of noise sensitivity and re-sampling instability.The feasibility and effectiveness of the proposed algorithm are verified on artificial datasets and multiple UCI datasets with different noise ratios.