分形理论下支持向量机核函数选择
|
摘要
支持向量机(support vector machine,SVM)是一种基于核的机器学习方法,不同的核函数对SVM的性能影响显著,如何针对具体问题获得一种有效的核函数选择方法成为SVM研究领域的一个重要问题。目前核函数选取仍是一个开放性的问题,存在着一系列的偶然性和局限性。而针对相对复杂问题时,使用何种类型的单一基核函数难以反映出其分布特征。因此,提出一种基于分形理论的核函数选择方法,在考虑不同核函数度量特征的同时,结合具体问题样本分布特征合理构造或选择核函数类型,并通过数据仿真以及相似性对比验证了算法的合理性。
Support vector machine( SVM) is a kernel-based machine learning method. Different kernel functions have a significant impact on the performance of SVM. How to obtain an effective kernel function selection method for specific problems has become an important issue in the field of SVM research. At present,the selection of kernel function is still an open issue,with a series of contingencies and limitations. However,it is difficult to reflect the distribution characteristics of any type of single basis kernel function for relatively complex problems.Therefore,a kernel function selection method based on the fractal theory is proposed. While considering the metric features of different kernel functions,the core function type can be reasonably constructed or selected based on the sample distribution characteristics of specific problems. The rationality of the algorithm was verified by data simulation and similarity comparison.
Support vector machine( SVM) is a kernel-based machine learning method. Different kernel functions have a significant impact on the performance of SVM. How to obtain an effective kernel function selection method for specific problems has become an important issue in the field of SVM research. At present,the selection of kernel function is still an open issue,with a series of contingencies and limitations. However,it is difficult to reflect the distribution characteristics of any type of single basis kernel function for relatively complex problems.Therefore,a kernel function selection method based on the fractal theory is proposed. While considering the metric features of different kernel functions,the core function type can be reasonably constructed or selected based on the sample distribution characteristics of specific problems. The rationality of the algorithm was verified by data simulation and similarity comparison.
引文
1郝云霄,闫楚良,刘克格.基于支持向量机的机翼载荷模型研究.科学技术与工程,2013,13(25):7432-7437Hao Yunxiao,Yan Chuliang,Liu Kege. Research on wing load model based on support vector machine[J]. Science Technology and Engineering,2013,13(25):7432-7437
2 陈鹏,胡啸峰,陈建国.基于模糊信息粒化的支持向量机在犯罪时序预测中的应用.科学技术与工程,2015,15(35):54-57,63Chen Peng,Hu Xiaofeng,Chen Jianguo. Application of support vector machine based on fuzzy information granulation in crime time series prediction[J]. Science Technology and Engineering,2015,15(35):54-57,63
3 王振武,孙佳骏,于忠义,等.基于支持向量机的遥感图像分类研究综述[J].计算机科学,2016,43(9):11-17,31Wang Zhenwu,Sun Jiajun,Yu Zhongyi,et al. Review of remote sensing image classification based on support vector machine[J].Computer Science,2016,43(9):11-17,31
4 贾亮,尹伊,杨慧超.基于分形维数的带噪语音端点检测[J].沈阳航空航天大学学报,2017,34(5):63-67Jia Liang,Yin Yi,Yang Huichao. Speech-based endpoint detection based on fractal dimension[J]. Journal of Shenyang Aerospace University,2017,34(5):63-67
5 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):1169-117Ni Zhiwei,Xiao Hongwang,Wu Zhangjun,et al. Attribute selection method based on improved discrete firefly swarm optimization algorithm and fractal dimension[J]. Pattern Recognition and Artificial Intelligence,2013,26(12):1169-1178
6 郑殿春,丁宁,沈湘东,等.基于分形理论的尖-板电极短空气隙放电现象[J].物理学报,2016,65(2):241-247Zheng Dianchun,Ding Ning,Shen Xiangdong,et al. Short-slip discharge phenomenon of tip-plate electrode based on fractal theory[J].Acta Physica Sinica,2016,65(2):241-247
7 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):914-919,926Li Qianqian,Li Chun,Yang Yang. Application of self-similarity and fractal dimension in wind field analysis[J]. Journal of Dynamic Engineering,2016,36(11):914-919,926
8 曾剑飞,何律君.分形理论在语音信号端点检测及增强中的运用[J].电脑知识与技术,2018,14(2):154-155,163Zeng Jianfei,He Lüjun. The application of fractal theory in endpoint detection and enhancement of speech signals[J]. Computer Knowledge and Technology,2018,14(2):154-155,163
9 赵莉华,丰遥,谢荣斌,等.基于振动信号分形维数的变压器松动诊断方法[J].电测与仪表,2018,55(03):7-12,19Zhao Lihua,Feng Yao,Xie Rongbin,et al. Transformer loose diagnosis method based on fractal dimension of vibration signal[J]. Electrical Measurement&Instrumentation,2018,55(03):7-12,19
10 单家俊,龙伦海,杨成,等. 2类变形Sierpinski地毯的Hausdorff维数[J].海南大学学报(自然科学版),2016,34(01):7-11Shan Jiajun,Long Lunhai,Yang Cheng,et al. Hausdorff dimension of two types of deformed Sierpinski carpets[J]. Joumal of Hainan University(Natural Science),2016,34(01):7-11
11 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):25-28Wang Tinghua,Chen Junting. Progress in the measurement of kernel function[J]. Application Research of Computers,2011,28(1):25-28
12 吴陈,孙伟.基于单核和组合核函数在垃圾邮件过滤中的比较应用[J].电子设计工程,2015,23(11):51-53Wu Chen,Sun Wei. Comparison of single core and combined kernel functions in spam filtering[J]. Electronic Design Engineering,2015,23(11):51-53
13 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):1135-1141Liang Liming,Zhong Zhen,Chen Zhaoyang. Research and Simulation of Support Vector Machine Kernel Function Selection[J]. Computer Engineering and Science,2015,37(6):1135-1141
14 代照坤,刘辉,王文哲,等.基于谱特征嵌入的脑网络状态观测矩阵降维方法[J].计算机应用,2017,37(8):2410-2415Dai Zhaokun,Liu Hui,Wang Wenzhe,et al. Dimensionality reduction method of brain network state observation matrix based on spectral feature embedding[J]. Journal of Computer Applications,2017,37(8):2410-2415
15 樊利,林满山.基于信息熵与Mahout的推荐算法的研究[J].计算机与数字工程,2017,45(10):1903-1906Fan Li,Lin Manshan. Research on recommendation algorithm based on information entropy and Mahout[J]. Computer and Digital Engineering,2017,45(10):1903-1906
2 陈鹏,胡啸峰,陈建国.基于模糊信息粒化的支持向量机在犯罪时序预测中的应用.科学技术与工程,2015,15(35):54-57,63Chen Peng,Hu Xiaofeng,Chen Jianguo. Application of support vector machine based on fuzzy information granulation in crime time series prediction[J]. Science Technology and Engineering,2015,15(35):54-57,63
3 王振武,孙佳骏,于忠义,等.基于支持向量机的遥感图像分类研究综述[J].计算机科学,2016,43(9):11-17,31Wang Zhenwu,Sun Jiajun,Yu Zhongyi,et al. Review of remote sensing image classification based on support vector machine[J].Computer Science,2016,43(9):11-17,31
4 贾亮,尹伊,杨慧超.基于分形维数的带噪语音端点检测[J].沈阳航空航天大学学报,2017,34(5):63-67Jia Liang,Yin Yi,Yang Huichao. Speech-based endpoint detection based on fractal dimension[J]. Journal of Shenyang Aerospace University,2017,34(5):63-67
5 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):1169-117Ni Zhiwei,Xiao Hongwang,Wu Zhangjun,et al. Attribute selection method based on improved discrete firefly swarm optimization algorithm and fractal dimension[J]. Pattern Recognition and Artificial Intelligence,2013,26(12):1169-1178
6 郑殿春,丁宁,沈湘东,等.基于分形理论的尖-板电极短空气隙放电现象[J].物理学报,2016,65(2):241-247Zheng Dianchun,Ding Ning,Shen Xiangdong,et al. Short-slip discharge phenomenon of tip-plate electrode based on fractal theory[J].Acta Physica Sinica,2016,65(2):241-247
7 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):914-919,926Li Qianqian,Li Chun,Yang Yang. Application of self-similarity and fractal dimension in wind field analysis[J]. Journal of Dynamic Engineering,2016,36(11):914-919,926
8 曾剑飞,何律君.分形理论在语音信号端点检测及增强中的运用[J].电脑知识与技术,2018,14(2):154-155,163Zeng Jianfei,He Lüjun. The application of fractal theory in endpoint detection and enhancement of speech signals[J]. Computer Knowledge and Technology,2018,14(2):154-155,163
9 赵莉华,丰遥,谢荣斌,等.基于振动信号分形维数的变压器松动诊断方法[J].电测与仪表,2018,55(03):7-12,19Zhao Lihua,Feng Yao,Xie Rongbin,et al. Transformer loose diagnosis method based on fractal dimension of vibration signal[J]. Electrical Measurement&Instrumentation,2018,55(03):7-12,19
10 单家俊,龙伦海,杨成,等. 2类变形Sierpinski地毯的Hausdorff维数[J].海南大学学报(自然科学版),2016,34(01):7-11Shan Jiajun,Long Lunhai,Yang Cheng,et al. Hausdorff dimension of two types of deformed Sierpinski carpets[J]. Joumal of Hainan University(Natural Science),2016,34(01):7-11
11 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):25-28Wang Tinghua,Chen Junting. Progress in the measurement of kernel function[J]. Application Research of Computers,2011,28(1):25-28
12 吴陈,孙伟.基于单核和组合核函数在垃圾邮件过滤中的比较应用[J].电子设计工程,2015,23(11):51-53Wu Chen,Sun Wei. Comparison of single core and combined kernel functions in spam filtering[J]. Electronic Design Engineering,2015,23(11):51-53
13 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):1135-1141Liang Liming,Zhong Zhen,Chen Zhaoyang. Research and Simulation of Support Vector Machine Kernel Function Selection[J]. Computer Engineering and Science,2015,37(6):1135-1141
14 代照坤,刘辉,王文哲,等.基于谱特征嵌入的脑网络状态观测矩阵降维方法[J].计算机应用,2017,37(8):2410-2415Dai Zhaokun,Liu Hui,Wang Wenzhe,et al. Dimensionality reduction method of brain network state observation matrix based on spectral feature embedding[J]. Journal of Computer Applications,2017,37(8):2410-2415
15 樊利,林满山.基于信息熵与Mahout的推荐算法的研究[J].计算机与数字工程,2017,45(10):1903-1906Fan Li,Lin Manshan. Research on recommendation algorithm based on information entropy and Mahout[J]. Computer and Digital Engineering,2017,45(10):1903-1906