基于分形理论的支持向量机核函数选择  

The Selection of SVM Kernel Function Based on Fractal Theory

作　　者：梁礼明 陈明理 刘博文 吴健 LIANG Liming;CHEN Mingli;LIU Bowen;WU Jian(School of Electrical Engineering and Automation,Jiangxi University of Science and Technology,Ganzhou Jiangxi 341000,China)

机构地区：[1]江西理工大学电气工程与自动化学院,江西赣州341000

出　　处：《江西师范大学学报（自然科学版）》2019年第3期309-313,319,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(51365017);江西省自然科学基金(20132BAB203020);江西省教育厅科学技术研究(GJJ170491)资助项目

摘　　要：核方法是机器学习领域内的研究热点之一,在处理非线性和高维数据问题中表现出许多优势,已被广泛应用于分类、回归等领域.支持向量机是最具代表性的核方法,而不同的核函数具有各异的度量特征,故核函数的选择对支持向量机泛化能力有着重要的影响.而目前核函数的选择仍是一个开放性的问题,存在着一系列的偶然性和局限性.该文利用分形几何分析数据蕴含的特征信息来有指导性地选择核函数,以提高支持向量机的泛化能力,并通过实例仿真验证该方法是有效可行的.As one of the research focuses in machine learning,Kernel method has been widely applied in classification,regression and some other fields due to its a great deal of advantages in dealing with nonlinear and high-dimensional data problems.Support Vector Machine (SVM) is the most representative method,and different kernel functions have different measurement features.Therefore,the selection of kernel function has an important influence on the generalization capability of SVM.However,kernel function selection is still an open problem at present,and there exists the contingency and limitations which the process reveals.In order to improve the generalization ability of SVM,the kernel function is selected by using the adjustment information of fractal geometry analysis data and the simulation results show that the method is effective and feasible.

关 键 词：核方法 支持向量机 核函数 分形几何 分形维数 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]