The Improve Research Of Non-positive Kernel Regression Machine

Support Vector Machine (SVM) is a widespread learning approach based on statistical learning theory, which has obtained its practical applications in many areas such as pattern recognition, regression analysis and prediction, and density evaluation due to its excellent generalized capability. When SVM applied in regression and prediction, we often call that support vector regression machine as SVR. Usually, in the area of regression analysis, The research of machine learning methods are based on that kernel function must be positive definite, it just means that kernel function must be satisfied Mercer conditions. However, in some certain specific areas, kernel function can not be guaranteed as positive definite kernel function, such as Sigmoid kernel function in neural networks. And in practical applications, it's difficult to check kernel function is a positive one or not, except kernel function was known by people already. The main purpose of this paper is to research the method of non-positive kernel for SVR.First of all, based on the study of Non-Positive Kernel Regression Machine method, we propose Improved Non-Positive Kernels Machine Regression method which each sample regression error must be constrained besides total regression error was constrained. It have improved NPKMR method's regression accuracy and generalization performance.Secondly, we propose SMO algorithms for Support Vector Regression with Non-Positive kernel. By use decomposition method of SMO algorithm and SupportVector Regression machine model's constraints, translated SVR model to a series seek the minimum problem of parabolic within a given interval to solving Support Vector Regression of Non-Positive kernel.Finally, by using Boston Housing and Abalones data sets to empirical analysis with INPMR method and SMO algorithm for sloving non-positive kernel SVR, And then compared prediction results of NPKMR method and standard SVR method. Evaluation INPMR method and SMO algorithm for sloving non-positive kernel SVR's feasibility and performance.