支持向量机中核函数和参数选择研究及其应用
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摘要
支持向量机(Support Vector Machine,SVM)是二十世纪九十年代发展起来的统计学习理论的重要内容,它是由AT&T Bell实验室的V.Vapnik等人提出的一种针对分类和回归问题的新型机器学习方法,它借助于最优化方法解决机器学习问题,集成了最优超平面、Mercer核函数、凸二次规划、稀疏解和松弛变量等多项技术,具有全局最优、结构简单、推广能力强等优点,在模式分类、回归分析和概率密度估计等若干方面获得非常好的应用效果。然而,支持向量机还处于不断发展和完善之中。本文针对SVM的模型、核函数的构造、SVM参数选择和孤立点检测四个方面进行了研究。具体内容如下：
一、概述了本文研究内容的基础—统计学习理论与支持向量机方法,描述并比较了目前研究与应用较多的几种训练算法和变形算法,为本文后续的研究内容进行了铺垫。
二、引入模糊逻辑思想,提出了基于高斯核函数和Sigmoid核函数、高斯核函数和模糊Sigmoid核函数的两种新的混合核函数。这两种混合核函数集聚了局部核函数和全局核函数的优点,提高了SVM算法的学习精度并减少了学习时间。实验结果表明,基于这两种混合核函数的SVM,不论在分类精度还是分类时间上都优于传统基于单一核函数的SVM算法。
三、在传统遗传算法与梯度算法的基础下,提出了一种自适应混合遗传算法并应用于支持向量机的模型参数选择研究中。仿真实验表明了该算法应用于SVM模型参数选择中选出的参数比传统的遗传算法、交叉验证和网格搜索等算法选择出的参数都要好,提高了SVM的识别精度。
四、根据ε—SVR和v—SVR中的参数ε和v的特殊意义,提出了基于ε—SVR的回归分析中的孤立点检测方法和基于v—SVR的回归分析中的孤立点检测方法。实验结果表明,提出的基于ε—SVR的回归分析中的孤立点检测方法和基于v—SVR的回归分析中的孤立点检测方法可以准确有效地检测出回归分析过程中的孤立点。
Support Vector Machine (SVM) developed to be the core of statistical learning theory in 1990s, it is a new machine learning method proposed by V.Vapnik of AT&T Bell Laboratories, which solves machine learning problems by means of optimization methods, integrates optimal hyperplane, mercer kernel function, convex quadratic programming, sparse solutions and relaxation etc. several techniques, with the good values of global optimum, simple structure and strong ability to promote. It has some good results in many aspects, such as pattern classification, regression analysis and probability density estimation.However, SVM still has a long way to go. This paper does the researches on four areas:SVM model, kernel function constructing, SVM parameter selection and outlier detection. Details are as follows:
First, outlining the basis of the research-statistical learning theory and support vector machine approach, described and compared several training algorithm and distortion algorithm, bedded for the follow-up research content.
Second, this paper introduced the fuzzy logic theory, proposed two new hybrid kernel functions based on gaussian kernel function, sigmoid kernel function and gaussian kernel function fuzzy sigmoid kernel function. The two new hybrid kernel functions integrated the benefits of local and global nuclear functions, improved the learning accuracy and reduced time of SVM. Experimental results show that the proposed two mixed kernel functions are better than the traditional nuclear function whether in classification accuracy or classification time.
Third, proposed an adaptive hybrid genetic algorithm based on traditional genetic algorithm and gradient algorithm, which applied to the research of the model parameters selection of support vector machine. Simulation results show that the parameters selected by this algorithm are better than the parameters selected by the tranditional genetic algorithm, cross validation and grid search algorithm, improves the recognition accuracy of SVM.
Fourth, proposed two isolated-points-detect methods in regression analysis, based on the isolated-points-detect methods inε-SVR and v-SVR regression analysis.The experiment results show that, the two methods can detect the isolated-points accurately and effectively.
一、概述了本文研究内容的基础—统计学习理论与支持向量机方法,描述并比较了目前研究与应用较多的几种训练算法和变形算法,为本文后续的研究内容进行了铺垫。
二、引入模糊逻辑思想,提出了基于高斯核函数和Sigmoid核函数、高斯核函数和模糊Sigmoid核函数的两种新的混合核函数。这两种混合核函数集聚了局部核函数和全局核函数的优点,提高了SVM算法的学习精度并减少了学习时间。实验结果表明,基于这两种混合核函数的SVM,不论在分类精度还是分类时间上都优于传统基于单一核函数的SVM算法。
三、在传统遗传算法与梯度算法的基础下,提出了一种自适应混合遗传算法并应用于支持向量机的模型参数选择研究中。仿真实验表明了该算法应用于SVM模型参数选择中选出的参数比传统的遗传算法、交叉验证和网格搜索等算法选择出的参数都要好,提高了SVM的识别精度。
四、根据ε—SVR和v—SVR中的参数ε和v的特殊意义,提出了基于ε—SVR的回归分析中的孤立点检测方法和基于v—SVR的回归分析中的孤立点检测方法。实验结果表明,提出的基于ε—SVR的回归分析中的孤立点检测方法和基于v—SVR的回归分析中的孤立点检测方法可以准确有效地检测出回归分析过程中的孤立点。
Support Vector Machine (SVM) developed to be the core of statistical learning theory in 1990s, it is a new machine learning method proposed by V.Vapnik of AT&T Bell Laboratories, which solves machine learning problems by means of optimization methods, integrates optimal hyperplane, mercer kernel function, convex quadratic programming, sparse solutions and relaxation etc. several techniques, with the good values of global optimum, simple structure and strong ability to promote. It has some good results in many aspects, such as pattern classification, regression analysis and probability density estimation.However, SVM still has a long way to go. This paper does the researches on four areas:SVM model, kernel function constructing, SVM parameter selection and outlier detection. Details are as follows:
First, outlining the basis of the research-statistical learning theory and support vector machine approach, described and compared several training algorithm and distortion algorithm, bedded for the follow-up research content.
Second, this paper introduced the fuzzy logic theory, proposed two new hybrid kernel functions based on gaussian kernel function, sigmoid kernel function and gaussian kernel function fuzzy sigmoid kernel function. The two new hybrid kernel functions integrated the benefits of local and global nuclear functions, improved the learning accuracy and reduced time of SVM. Experimental results show that the proposed two mixed kernel functions are better than the traditional nuclear function whether in classification accuracy or classification time.
Third, proposed an adaptive hybrid genetic algorithm based on traditional genetic algorithm and gradient algorithm, which applied to the research of the model parameters selection of support vector machine. Simulation results show that the parameters selected by this algorithm are better than the parameters selected by the tranditional genetic algorithm, cross validation and grid search algorithm, improves the recognition accuracy of SVM.
Fourth, proposed two isolated-points-detect methods in regression analysis, based on the isolated-points-detect methods inε-SVR and v-SVR regression analysis.The experiment results show that, the two methods can detect the isolated-points accurately and effectively.
引文
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[2]李裕奇.应用概率论与数理统计.成都：成都科技大学出版社,1997,133-135
[3]伊亨云,朱金明,孙荣恒.概率论与数理统计.重庆：重庆大学出版社,1995,122-130
[4]F.Rosenblatt.Principles of Neurodynamics:Perception and Theory of BrainMechanisms.Spartan Book,Washington DC,1962,1-5
[5]B.J.Novikoff. On convergence proofs on perceptrons.in Proceedings of the Symposium on the Mathematical Theory of Autodata,Polytechnic Institute of Brooklyn,1962.12,515-622
[6]V.N.Vapnik. Statistical Learning Theory.New York:Wiley,1998
[7]B.E.Boser,I.M.Guyon,V.N.Vapnik.A training algorithm for optimal margin classifiers In Proceedings of the 5th annual ACM Workshop on computation learning theory.ACM Press.1992,144-152
[8]V.Vapnik. Support vector method.Lecture Notes in Computer Science,1997,Vol.1327:263
[9]Gustavo.CV, Luis.GC,etal.Composite kernels for hyperspectral image classification. IEEE science and Remote Sensing Letters,2006,3(1):93-98
[10]Lodhi H,Saunders C,Shawe-Taylor J,etal.Text classification using string kernel Journal of Machine Learning Research,2002,2(2):419-444
[11]Cortes Corinna, Vapnik Vladimir.Support-vector networks Source.Machine Learning.Sep,1995, 20(3):273
[12]Scholkopf B.Estimating the support of high-dimensional distribution.Technical Report, Microsoft Research,1999,87-99.
[13]E.Osuna.An Improved Training Algorithm for Support Vector Machines [J].In Proc.IEEE Neural Networks in Signal Processing.1997,97
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[15]邵小健.支持向量机中若干优化算法研究[学位论文][D].山东：山东科技大学,2002
[16]Yi Liu,Zheng Y.F.Soft SVM and its application to video object extraction,In Proceedings of(ICASSP'05)IEEE International Conference on Acoustics,Speech,and SignaProcessing,18-23 March 2005,5:193-196
[17]Lin Chun-Fu, Wang Sheng-De.Fuzzy support vector machines.IEEE Transactions on Neural Networks,March 2002,13(2):464-471
[18]边肇祺,张学工.模式识别[M].第2版.北京：清华大学出版社,1999
[19]张学工.关于统计学习理论和支持向量机[J].自动化学报,2000,26(1)：32-41
[20]张润楚.多元统计分析.科学出版社,2006.9
[21]阎辉,张学工,马云潜,李衍达.基于变异函数的径向基核函数参数估计.自动化学报,2002,28(3)：450—455
[22]Mika S, Ratsch G.Weston J etal.Fisher Diseriminant Analysis With Kernels.Neural Networks for Signal Proeessing 9.NewYork:IEEE Press,1999:41-48
[23]Scholkopf B,Smola A,Muller KR.Kernel Principal component analysis.In Scholkopf B,Burges CJC,& A.J.Smola,editors,Advanced in Kernel Method-Support Vector Machine.MIT Press, Cambridge,MA,1999:327-352
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[25]Platt J C.Using analytic QP and sparseness to speed training support vector machines.Advance in Neural Information Processing Systems,MITpress,1999:557-563
[26]Chapelle O, Vapnik V.Model selection for support vector machines,Advance in The Neural Information Processing Systems,S A Solla,MA:MIT Press,2000:230-236
[27]Cherkassky V, Ma Y Q.Practical slection of SVM parameters and noise estimation for SVM regression,Neural Networks,2004,17(1):113-126
[28]M.Seeger.Guassian Proeesses of machine learning[J].International Journal of Neural Systems.2004,142:69-106
[29]Lee J Keerthi.Automatic model selection for support vector machines,Technical Report,Dept.of Computer Science and information Engineering,National Taiwan University,Taipei.2000,(11)
[30]Gold C, Sollish P.Model selection for support vector machine classification Neurocomputeing, 2003,55(1-2):221-249
[31]BengioY.Gradient based optimization of hyperparameters, Neural Computation,2000,12(8): 1889-1990
[32]N.Ito, J.Nakano.An Introduction to Support Vector Machines and Other Kernel based Learning Methods.New York:Cambridge University Press,2000
[33]U.Luxburg, O.Bousquet,B.Scholkopf.A compression approach to SVM model seletion[J].Journal of Machine Learning Researeh.2004,5:293-323
[34]姚全珠,田元.基于人工免疫的支持向量机模型选择算法.计算机工程,第34卷第15期
[35]吴高巍,陶卿,王珏.基于后验概率的支持向量机.计算机研究与发展.42(2)：196-202,2005
[36]郭辉,刘贺平,王玲.最小二乘支持向量机参数选择方法及其应用研究.系统仿真学报.第18卷第7期.2006年7月
[37]刘向东,骆斌,陈兆乾.支持向量机最优模型选择的研究.计算机研究与发展,42(4)576-5812005.
[38]阎国华,朱永生.支持向量机回归的参数选择方法.计算机工程.第35卷第13期2009年7月
[39]Qi Miao, Shi-Fu Wang.Nonlinear Model predietive Control Based on Support Vector Regression .In Proeeeding of International Conference on Maehine Learning,2002,3:1657-1661
[40]Kruif BJ, Vries TJA. On using a support vector machine in Learning Feed-Forward Control.In Proeeedings of int on Advanced Intelligent Meehatronies, Como, Italy, July.2001:272-277
[41]Suykens JAK.Nonlinear Modeling and Support Vector Maehines In Proeeedings Of the 18th instrumentation and Measurement Technology Conference,2001:287-294
[42]Ryehetsky M, Ortmann S,Glesner M.Support Vector Approaches for Engine Knock Detection.International Joint Conference on Neural Networks,1999,2:969-974.
[43]李凌均,张周锁,何正嘉.基于支持向量机的机械故障智能分类研究.小型微型计算机系统,2004,25(4)：667-670
[44]王成栋,朱永生,张优云等.时频分析与支持向量机在柴油机气阀故障诊断中的应用.内燃机学报,2004,22(3)：245-251
[45]Osuna E, Freund R, Girosi F.Training support vector machines:an application to face detection.In:Proc. Computer version and Pattern Recognition,1997:130-136
[46]Schmidt M.Identifying speaker with support vector network.In Interface Proceedings. Sydney
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