支持向量机核函数选择方法探讨

【作者】 冯新刚；

【导师】 梁礼明；

【作者基本信息】 江西理工大学 ， 控制理论与控制工程， 2012， 硕士

【摘要】 支持向量机学习方法的理论基础是统计学习理论,该方法继承了统计学习理论的许多优秀的概念,比如VC维概念,结构风险最小原理等,在此基础上提出最优超平面概念,用于计算基于最优超平面的决策函数；同时引入核函数后,使得非线性映射绕过高维空间,避免“维数灾难”,计算更加方便,从而可以得到较为理想的泛化能力。对于非线性可分的样本集,合理选择核函数可以提高其映射的线性化程度,增强可分性和预测能力。因此,核函数的选择及核函数中相关参数的选择对样本线性可分的作用很大。不同形式的核函数,由于其自身的特点不同,使其对非线性样本的映射效果有所不同,因此,怎样选择合适的核函数是SVM学习方法中十分重要的研究课题。针对核函数的选择问题,本文着重做了以下研究内容：一是原始样本数据分布特征的数学描述方法的研究；二是基于样本分布特征数学描述出发,根据样本不同分布特征来选取合适的核基函数；是在核基函数选择方法研究的基础上,阐述了一种核基函数优化组合方法,即利用数据分布特征选择各个子集的核基函数,再进行核基函数的线性组合：四是介绍了一种利用核矩阵的秩差异度选择核函数组合的方法。这种方法先把预选的几种核函数组合映射得到核矩阵,再通过计算各核矩阵的秩差异度来选择合适的核函数组合。对以上核函数选择方法的研究结果,均进行了相应的仿真实验。实验证明,以上方法对SVM学习方法的泛化能力有明显提高,方案是切实可行的。通过以上内容的研究,丰富了核函数选择方法,有助于SVM学习能力和泛化能力的提高,具有一定的工程推广价值。更多还原

【Abstract】 Support Vector Machine is a new machine learning method based on Statistical Learning Theory. The method inherited the many excellent concept of statistical learning theory, such as VC dimension, the theory of minimum structure risk. The theory as a foundation, puts forward the optimal hyperplanes concept, used to generate decision function. Kernels are used in SVM to map the learning data (non-linearly) into a higher dimensional feature space where the computational power of the linear learning machine is increased, It can get rid of the "dimension disaster" problem. A kind of good method SVM used in the small sample, non-linearly sample and High dimensional pattern recognition. The Logical Choice of kernel function can increase the mapping of linear degree. So, the Choice of kernel function and related parameters is important to improve the Sample separability.Every kernel function has its advantages and disadvantages, its to the effect of mapping non-linearity samples is different, the method of selection kernel function in the study of SVM is very-important. The contents of my paper is introduced to the method of selection kernel function based on the distribution characteristics of samples. First of all, the paper analyze the distribution characteristics of samples base on Mathematics description method, secondly, According to different distribution characteristics to select the kernel function; and then, the introduction of the combination of kernel function selection metho base on it, experiments show that the SVM classifier generalization ability have increased significantly; Finally, the paper introduces a kind method of selection kernel function combinations base on rank diversity of kernel matrices. These research results, do the simulation experiment.Through these content of research, increase the method of selection kernel function, SVM learning ability and generalization ability was improved.更多还原