Linear Programming Support Vector Regression Algorithm With Given Empirical Risk

SVM (Support Vector Machine, referred to as SVM) is based on Statistical LearningTheory (Statistical Learning Theory, referred to as SLT) by an American N Vapnikprofessor in the1990s, put forward a kind of Machine Learning methods, the method ofstudy is based on Statistical Machine Learning Theory, developed for small sample situationspecifically. VC in support vector machine (SVM) is based on the statistical learning theoryand structural risk minimization principle based on the part of the most practical, the originalis mainly used to deal with the classification of the sample problem, its main idea is to thestructural risk minimization principle of statistical learning theory reference, it can not onlydeal with linear, but also process the nonlinear case. In nonlinear separable case, by using thekernel function, the original space of the sample data is mapped to a high-dimensional featurespace, make it in the high dimensional feature space linear separable, and the method of usinglinear separable to find the optimal solution. Kernel function method is used to calculate theinner product, also can greatly avoid "dimension disaster". With the continuous developmentof science and technology, on the basis of the classification problem with effective algorithm,support vector machine (SVM) extension to regression problems, therefore, the support vectorregression machine. Support vector regression machine in processing on the issue of functionfitting effect has important theoretical significance and wide application prospect. It isbecause of the support vector machine has the good study performance and generalizationability, so this technology has been successfully applied in many fields.Support vector machine (SVM) algorithm can not only deal with classification problem,but also can deal with regression problems. Based on support vector machine (SVM)classification and regression theory,on the basis of determining the empirical risk level underthe linear programming support vector regression algorithm research. The traditional supportvector regression algorithm, the empirical risk and confidence need a compromise parameterC to control risk, and for different sample data, it is not easy to choose the optimal parameterC in general, when the parameter C value is bigger, the empirical risk plays a major role, onthe other hand, when the parameter C value is small, the requirement to the empirical risk isnot so high. C parameter selection method on predecessors have made some researchachievements, in the case of quadratic programming is proposed for a given level of risk ofsupport vector machine (SVM) classification and regression model, experience in a givenlevel of risk for the purpose of minimizing structural risk, on this basis, this paper extends theidea to the linear programming support vector regression model, is given to determine thelevel of empirical risk linear programming support vector regression algorithm, this algorithm can determine the size of the experience level of risk in advance, in addition, the newalgorithm can also by setting different sample points on the empirical risk, the size of theprocessing situation of the heteroscedasticity exists in the sample. Finally, the paper by fittinga regression function as an example, the application of the new algorithm presents asimulation experiment, proves the feasibility and effectiveness of the new algorithm.