Abstract: Based on the conditions of kernel function of Support Vector Machine（SVM）, the reproducing kernel function on the Sobolev Hilbert space and polynomial kernel function are combined efficiently. A new combined kernel function is given, and a model analysis method of combined kernel SVM based on reproducing kernel is proposed, which has the advantages of global kernel function and local kernel function, and the complexity of the algorithm is reduced. The simulation results show that the kernel function of SVM adopts combined kernel function which is based on the reproducing kernel is feasible. The kernel function not only has the nonlinear mapping characteristics, but also inherits good approximation of reproducing kernel function on the nonlinear characteristics step by step. The model analysis results are more delicate than individual kernels function.

Key words: Support Vector Machine（SVM）, reproducing kernel, combined kernel function, model analysis

摘要： 基于支持向量机核函数的条件，将Sobolev Hilbert空间的再生核函数和多项式核函数进行有效的线性组合，给出一种新的支持向量机的组合核函数，提出一种基于再生核的组合核函数支持向量机的模式分析方法，该方法兼具了全局核函数与局部核函数的优点，且算法的复杂度被降低。仿真实验结果表明：支持向量机的核函数采用基于再生核的组合核函数是可行的，且此核函数不仅具有核函数的非线性映射特征，而且也继承了核函数对非线性逐级精细逼近的特征，模式分析的效果比单核函数可以更加细腻。

关键词: 支持向量机, 再生核, 组合核函数, 模式分析