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

摘要： 基于支持向量机核函数的条件，将Sobolev Hilbert空间的再生核函数进行改进，给出一种新的支持向量机核函数，并提出一种改进的最小二乘再生核支持向量机的回归模型，该回归模型的参数被减少，且仿真实验结果表明：最小二乘支持向量机的核函数采用改进的再生核函数是可行的，改进后的再生核函数不仅具有核函数的非线性映射特征，而且也继承了该再生核函数对非线性逐级精细逼近的特征，回归的效果比一般的核函数更为细腻。

关键词: 支持向量机, 核函数, 再生核, 信号回归