Research On Robust Twin Support Vector Machine For Noise Data

Robustness is one of the hotspots in the field of machine learning and pattern recognition,which can ensure the stability of the model and alleviate the negative effects of outliers.As an effective tool for dealing with binary classification problems,twin support vector machine(TSVM)not only inherits the solid theoretical foundation of support vector machine(S VM),but also further reduces the computational cost,but it is still sensitive to noisy data,that is,its robustness still needs to be improved.Therefore,based on statistics and optimization theory,for the purpose of establishing a more robust classification model,this thesis establishes a twin support vector machine classification learning framework by looking for better distance measurement and loss function to ensure that it can effectively restrain the influence of noise and improve the classification performance,including:1.A robust twin support vector machine model based on capped linear loss function is proposed(recorded as Linex-TSVM).Firstly,the capped linear loss function(La,ε)is given,which has boundedness,non-convexity and robustness.In the two-classification task,Linex-TSVM can not only reduce the influence of outliers on Linex-SVM,but also improve the classification performance and robustness of Linex-SVM.In addition,the principle of structural risk minimization is realized by introducing two regularization terms to reduce the influence of outliers on the model.Finally,a simple and efficient iterative algorithm is designed to solve the non-convex optimization problem Linex-TSVM,and the time complexity of the algorithm is analyzed.It is proved that the model satisfies the Bayesian criterion.The results show that the proposed algorithm is comparable to the existing algorithms in terms of robustness and reliability.2.A capped robust twin boundary support vector machine(abbreviated as CRTBSVM)is proposed.CRTBSVM introduces the non-convex capped L2,p-norm distance metric,which overcomes the shortcomings of the capped L1-norm distance metric and the capped L2-norm distance metric,and further improves the generalization performance and robustness of the TSVM.CRTBSVM not only reduces the influence of outliers on TSVM,but also greatly improves the classification performance of TSVM.In addition,in order to inherit the excellent performance of CRTBSVM and further reduce its computational cost,a least square version of CRTBSVM,called fast capped robust twin boundary support vector machine(abbreviated as FCRTBSVM),is presented,and two efficient iterative algorithms are designed to solve the problem.At the same time,the local optimality,computational complexity and convergence of the two algorithms are rigorously analyzed and proved,and their performance is verified on multiple data sets,and the results show that the expected goal can be achieved.