基于分形理论的支持向量机核函数选择
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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.
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.
引文
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[3]刘高辉,杨星.一种混合核函数的支持向量机[J].微型机与应用,2017,36(11):19-22.
[4]宋晖,薛云,张良均.基于SVM分类问题的核函数选择仿真研究[J].计算机与现代化,2011(8):133-136.
[5]尹嘉鹏.支持向量机核函数及关键参数选择研究[D].哈尔滨:哈尔滨工业大学,2016.
[6]梁礼明,冯新刚,陈云嫩,等.基于样本分布特征的核函数选择方法研究[J].计算机仿真,2013,30(1):323-328.
[7]王振武,何关瑶.核函数选择方法研究[J].湖南大学学报:自然科学版,2018,45(10):155-160.
[8]Mehmani A,Chowdhury S,Meinrenken C,et al.Concurrent surrogate model selection(COSMOS):optimizing model type,kernel function,and hyper-parameters[J].Structural and Multidisciplinary Optimization,2018,57(3):1093-1114.
[9]Jayadeva.Learning a hyperplane classifier by minimizing an exact bound on the VC dimension[J].Neurocomputing,2015,149(3):683-689.
[10]刘学艺,宋春跃,李平.基于Vapnik-Chervonenkis泛化界的极限学习机模型复杂性控制[J].控制理论与应用,2014,31(5):644-653.
[11]倪志伟,肖宏旺,伍章俊,等.基于改进离散型萤火虫群优化算法和分形维数的属性选择方法[J].模式识别与人工智能,2013,26(12):1169-1178.
[12]邬啸,魏延,吴瑕.基于混合核函数的支持向量机[J].重庆理工大学学报:自然科学,2011,25(10):66-70.
[13]Wang Fuguang,He Ketai,Liu Ying,et al.Research on the selection of kernel function in SVM based facial expression recognition[EB/OL].[2018-03-02].http://ieeexplore.ieee.org/document/6566586/.
[14]汪廷华,陈峻婷.核函数的度量研究进展[J].计算机应用研究,2011,28(1):25-28.
[15]梁礼明,钟震,陈召阳.支持向量机核函数选择研究与仿真[J].计算机工程与科学,2015,37(6):1135-1141.
[16]李倩倩,李春,杨阳.自相似性和分形维数在风场分析中的应用[J].动力工程学报,2016,36(11):914-919,926.
[17]朱志宝,白永强.分形几何及其应用[J].价值工程,2012,31(35):5-7.
[18]申文栋,梁静.基于分形维数的GIS局部放电信号发展过程分析[J].机电信息,2011(3):62-63,65.
[19]Grassberger P,Procaccia I.Measuring the strangeness of strange attractors[J].Physica D:Nonlinear Phenomena,1983,9(1/2):189-208.