关键词: 支持向量机, 核函数, 再生核, 信号回归

Abstract: Based on the conditions of kernel function of support vector machine，reproducing kernel function on the Sobolev Hilbert space is improved，a new support vector machine kernel function is given，and an improved least squares reproducing kernel support vector machine regression model is proposed，the parameters of the improved model is reduced，the experimental results show the improved reproducing kernel which the least square support vector machine adopts is feasible，improved reproducing kernel function not only possesses the nonlinear mapping characteristics of the kernel function，but also succeeds to good approximation of reproducing kernel function on the nonlinear characteristics step by step，the regression results are more delicate than general kernels function.

Key words: Support Vector Machine（SVM）, kernel function, reproducing kernel, signal regression