【作者】 刘琰；

【导师】 周水生；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2012， 硕士

【摘要】 支持向量机（Support Vector Machine，SVM）是二十世纪九十年代发展起来的统计学习理论的核心内容，而核函数是支持向量机的主要组成部分，选择合适的核函数及其参数已经成为SVM进一步发展的关键点和难点。不同的核函数确定了不同的非线性变换和特征空间，同类满足Mercer条件的类核函数也有多种参数供选择。本文从以下两方面研究了高斯核函数和傅立叶核函数的性质及其应用：一方面，详细的研究了高斯核函数和傅立叶核函数的性能特征，证明了当参数在特定的范围内，基于该核函数的SVM取得有最优的分类错误率和最优支持向量，而参数超越此范围只会延长训练的时间，对支持向量机的性能没有额外的改进。另一方面，先引入了变形的傅立叶核函数，再分别研究了局部核，全局核特点；然后介绍了组合核函数的一般构造方法、具体形式及其优点，在此基础上提出两个新核函数：分别是改进的高斯核与多项式核凸组合，傅立叶核与Sigmoid核凸组合，仿真实验结果表明：新核函数具有较好的分类性能。更多还原

【Abstract】 Support Vector Machine(SVM) is the main content of Statistics Learning Theorydeveloped from1990s.Kernel function is the crucial ingredient of SVM. The selectionof the SVM-kernel with suitable form and parameters (Kernel Selection) has become akey-point both in theoretical research and application consideration. In fact, thenonlinear processing ability of SVM and the structure of the separating function areboth largely decided by the choice of individual kernel function. This paper studies theproperties and applications of Fourier kernel function and Gauss kernel function fromtwo aspects.On the one hand,we analyzes the nature of Gauss kernel and Fourier kernel indetail and show that: when the parameters of these kernels are in a specific range, SVMwith these kernel functions have the best classification error rate and optimal supportvectors. If the parameters are out of the range,it would only prolong the training time ofSVM, but the performance of SVM can not be improved additionally.On the other hand, we introduce a new variant Fourier kernel function,and analyzethe properties of the local kernel function and global kernel function.Then we alsodiscuss the characters of the form of the mixture kernels functions, and propose twonew types of mixture kernels functions. One is the conex combination of the improvedGauss kernel and Polynomial kernel,and the other one is the conex combination of Fouriorkernel and Sigmoid kernel. Experimental results show that the new mixture of kernelshave better classification performance.更多还原