【作者】 杨真真；

【导师】 李雷；

【作者基本信息】 南京邮电大学 ， 应用数学， 2011， 硕士

【摘要】 支持向量机(SVM)是在统计学习理论上发展起来的一种机器学习方法。由于较好的解决了小样本、非线性、高维数、局部极小值等问题以及具有良好的推广能力,SVM已经成为机器学习领域的一个研究热点。但传统的支持向量机对样本中的噪声和孤立点非常敏感,为了克服这个问题,提出了模糊支持向量机(FSVM)理论。在模糊支持向量机中如何构造合适的隶属度函数成为FSVM首要解决的问题。另外,如何从几何角度改进FSVM也已成为当今研究FSVM的又一个热点。本文详细论述了支持向量机理论、算法和性质,并通过构造合适的隶属度函数、核函数以及改进FSVM的几何结构,实现了对FSVM理论和算法的改进和完善。在对该课题进行深入研究后,主要做了如下创新性的工作:(1)用从信息几何角度构造的动态核函数表示样本点和类中心的距离以及样本间的密切度,即把核方法的思想引入到距离和密切度的表示中;(2)将基于类中心和密切度的模糊分类和回归隶属度函数分别进行组合,提出了基于类中心和密切度的乘积组合分类和回归隶属度函数,它们不仅考虑了样本点和类中心的距离,还考虑了样本间的密切度;(3)从几何角度改进L-1范数FSVR的惩罚项,提出了L-2范数FSVR,仿真实验结果显示它比SVR和L-1范数FSVR具有更好的回归精度;(4)提出了基于信息几何的模糊支持向量分类机和模糊支持向量回归机算法,并把基于信息几何的模糊支持向量分类机算法应用于图像边缘检测。更多还原

【Abstract】 Support Vector Machine (SVM) is a machine learning method based on statistical learning theory.Because it resolves the small sample, nonlinearity, high dimension and local minimum problemsperfectly and has good generalization ability, SVM has been a hot field of machine learning.However, tradition SVM is very sensitive to noises and outliers in the training sample, in order toovercome this problem, the fuzzy support vector machine (FSVM) is proposed. It is how toconstruct a suitable membership function that has been the primary problem in FSVM. In addition,how to promote FSVM from the geometry aspect has became another hot topic.This dissertation has elaborated the theory, algorithm and properties of SVM. The theory andalgorithm of FSVM perform more perfectly by constructing an appropriate membership function,kernel function and improving geometry of FSVM. After conducting a research deep into this topic,the main results are as follows:(1) Using the dynamic kernel function, which is constructed from information geometry aspect,to express the distance between sample points and their cluster centers and the affinity among thesample points, that is to say, the kernel method is introduced to the representation of distance andaffinity;(2) The product of combined fuzzy classification and regression membership function based onthe cluster center and the affinity are proposed. They are defined not only the distance between apoint and its cluster center, but also two different points of the sample, which is depicted as theaffinity between them;(3) L-2 norm fuzzy support vector regression is proposed from the geometry aspect. Thesimulation results show that it has better regression accuracy than support vector regression and L-1norm fuzzy support vector regression;(4) The algorithms of fuzzy support vector classification and fuzzy support vector regressionbased on information geometry are proposed. Then the fuzzy support vector classification algorithmis used to extract the edge of image.更多还原