The Research On Algorithm Of Support Vector Machine For Classification

SVM(support vector machine,SVM),is a novel tool to solve machine learning by means of optimization method.Because of its stronger generalization ability and easy operation of high-dimensional data,SVM has been widely researched and applied.although full-supervised support vector machine for classification can effectively solve various practical problems,but it needs experienced experts to tag the large unlabeled samples in order to get enough training samples,which will cost a lot of labor power and material resources.At the same time,there exist a lot of unmarked samples in real life.If these resources cannot be made full use of,then it can also lead to waste.Therefore,the researchers also presented support vector machine on the basis of semi-supervised learning according to the actual needs.However,the semi-supervised support vector machine(S3VM)is relatively new in the area of machine learning,and needs further research and improvement.The main research of the paper is presented as follows:Firstly,this paper studied the full-supervised support vector machine(SVM)model for classification.Aiming at low accuracy and poor efficiency of traditional support vector classification machine,two novel models are proposed in this paper.The one is a class of 1-norm Bezier function support vector machine model(BSSVM1)based on Bezier function and the other is a circle tangent smooth support vector machine(CTSSVM)based on the geometry of circle tangent.And their smoothness and convergence are proved and their approach performance to plus function is analyzed.Based on the characteristics of every model,the Armijo-Newton method and the BFGS method are used to solve respectively.Theoretical analysis and numerical experiment results prove that two novel model have a better classification performance than smooth models proposed previously.Secondly,in order to focus on the non-smooth and non-convex problems of the semi-supervised support vector machine in this paper,a piecewise function was proposed based on the analysis and studying on traditional models to approach the objective function of non-convex and non-smooth.The approach degree of the piecewise function to objective function could be chosen according to the accuracy demand.Therefore,a new piecewise smooth semi-supervised support vector machine(PWSS3VM)model based on piecewise function was introduced.And the low density separation(LDS)algorithm was applied to solving the model and its approximation performance to the symmetric hinge loss function was analyzed.Our theoretical analysis and numerical experiments confirm that PWSS3 VM model have a better classification performance and a higher classification efficiency than smooth models proposed previously.