【作者】 涂文根；

【导师】 韩国强； 袁华强； 熊金志；

【作者基本信息】 华南理工大学 ， 计算机应用技术， 2010， 硕士

【摘要】 作为数据挖掘的一种新方法,支持向量机从统计学习理论发展而来,是基于结构风险最小化原则设计的机器学习算法,很好地解决了传统机器学习算法所遇到的非线性、高维数、局部极小等问题。目前支持向量机已经得到了广泛的研究和应用,其最新的分支是光滑支持向量机,与支持向量机的传统算法和各种变形相比在学习速度上有较大的优势,同时有着更好的推广能力。该文从支持向量机的理论基础开始,简单阐述了统计学习理论的VC维理论和结构风险最小化原则,介绍了光滑支持向量机的最优化模型;分析了光滑支持向量机的光滑技术,包括Sigmoid函数的积分函数,基于圆弧曲线的分段函数和基于两插值点的插值多项式函数。本文重点研究了基于三个插值点的插值光滑技术,根据插值区间的不同分一般区间和基于原点的对称区间分别作了详细的探讨;给出了在对称区间插值求解最优插值多项式函数的详细求解过程,包括如何建立最优化模型和求解目标光滑函数;获得了最优三次二阶光滑多项式函数和最优四次二阶光滑多项式函数用于拟合光滑支持向量机的正号函数。另外还特别研究了基于三个插值点的一种间接插值情况,获得了一个一阶光滑的多项式函数。对文中重点研究的光滑函数有详细的求解过程;函数性能的理论证明;以及直观的函数曲线图。本文所研究的光滑函数都有严密的数学推导,以及对正号函数逼近性能的详尽理论证明。数据实验在模拟数据集上训练基于不同的光滑函数构建的各种光滑支持向量分类机;得出的结论是:总体上对正号函数逼近性能越好的光滑函数建立的光滑支持向量分类机的推广能力越好;计算越复杂的光滑函数构建的光滑支持向量分类机就会消耗越多的训练时间;因此必须衡量光滑函数对于正号函数的逼近效果和计算量才能获得最高训练效率和推广能力的光滑支持向量分类机。更多还原

【Abstract】 Support Vector Machines evolved from the Statistical Learning Theory is a new method for Data Mining. It’s a kind of machine learning algorithms based on Structural Risk Minimization. Comparing to the traditional machine learning algorithms, SVM is a good solution while encountered in non-linear, high dimension, local minimum and so on. SVM has been widely studied and applied recently, Smooth Support Vector Machine, a latest important branch of support vector machines, has better speed in learning comparing with traditional algorithms and deformations of SVM while it achieves better learning generalization ability.In this paper, theoretical foundation of SVM, mainly include the VC-dimensional theory and the principle of structural risk minimization in Statistical Learning Theory, will be introduced at beginning, as well as the model of SSVM. smooth techniques for SSVM, including the integral function of Sigmoid function initially proposed by SSVM, piecewise function based on sub-arc curve function and piecewise polynomial function will be anlysised. The main content of this paper is interpolation polynomial technology base on three interplation points, two situations including general region and symmertric region on both sides of the origin will be discussed. The courses of how to establish the optimization model and how to sovle the optimize problem for gaining the best polynomial functions in symmetric region will be given. Two 2-order smooth functions with three and four times, applying in SSVM, were got by the optimization model. A particular circumstance of indirectly interpolation base on three interpolation points is considered. For each smooth function in this paper, the theoretical basis, the detailed derivation process and performance are described.Base on simulated data, numerical experiment training smooth support vector classifier machine with all different kinds of smooth functions will be given. The better approximation for the plus function for the smooth function, the SSVM has better generalization ability, the more complex calculation for the smooth function, more training time will be consumed. So we should find a smooth function can achieve best generalization ability and least training time by balancing the approximation to the plus function and the calculation for the smooth function while in practical application.更多还原