L₀-sparse Dual Support Vector Machine And Its Applications

Support vector machine?SVM?,as an important method in machine learning area,has attracted much attention because of its good generalization ability,SVM can also be used to solve the problems of regression and classification.The SVM model is usually a convex quadratic programming problem with inequality constraints.By squaring the errors in the model and transforming the inequality constraints into equality constraints,the SVM model can be simplified into least squares support vector machine?LSSVM?.Besides,LSSVM also inherits the advantage of the strong generalization ability of SVM and kernel function to deal with nonlinear problems.Compared with SVM,the solution form of LSSVM model can be equivalent to the solution of linear equations,which is relatively simple.However,due to the LSSVM model transforms the non negative error term of the SVM model into the squared term of the error in the process of transforming the SVM model,that leads to the loss of sparse in the solution vector of the LSSVM model,which means that almost all the samples are used as support vectors to be calculated.Therefore,how to achieve more sparse support vector of LSSVM model is particularly important.This paper mainly introduces how to construct a new method to control the sparsity of support vector in LSSVM on the problems of regression and classification,and introduces its solving algorithm.What's more,the applications of the constructed models in the real financial area and credit default classification are studied.The research contents of this paper mainly have two aspects:Firstly,we consider the dual problems of LSSVM regression and classification models.The ₀l-sparse dual support vector machine models are constructed by adding l₀-norm constraint on the dual problems of regression and classification problems.We use sparse projection gradient?SPG?algorithm to solve constructed models.Secondly,we apply the models to the fitting regression,financial time series forecasting,hyperbolic screw binary classification problem and the discriminate prediction problem of credit customer default or not.The numerical experiments coding in Matlab prove that the constructed model can not only ensure accuracy,but also achieve sparser support vectors.Besides,we analysis the numerical results in solving index tracking problem by using l₀-sparse SVR model.The paper is organized as follows:The first chapter of this paper briefly introduces the development status of the LSSVM,SVM and the sparse optimization researches.The second chapter mainly introduces the basic LSSVM model and the corresponding solving method of least squares support vector machine.The third chapter introduces the proposed ₀l-sparse dual support vector machine model and the sparse projection gradient algorithm.The fourth chapter is the model applications of practical problems and its coresponding numerical experiments.Last part is the summary and prospect of the thesis.