最小二乘支持向量回归滤波系统性能分析
摘要
支持向量机(Support Vector Machine:SVM)一直作为机器学习方法在统计学习理论基础上被研究和发展,本文从信号与系统的角度出发,证明了平移不变核最小二乘支持向量机(Least Squares SVM:LS-SVM)是一个线性时不变系统.以Ricker子波核为例,探讨了不同参数对最小二乘支持向量回归(Least Squares Support VectorRegression:LS-SVR)滤波器频率响应特性的影响,这些参数的不同选择相应地控制着滤波器通带上升沿的陡峭性、通带的中心频率、通带带宽以及信号能量的衰减,即滤波器长度越长通带的上升沿越陡,核参数值越大通带的中心频率越高,且通带带宽越宽,正则化参数值越小,通带带宽越窄(但通带中心频率基本保持恒定),有效信号幅度衰减越严重.合成地震记录的仿真实验结果表明,Ricker子波核LS-SVR滤波器在处理地震勘探信号的应用中,滤波性能优于径向基函数(Radial Basic Function:RBF)核LS-SVR滤波器以及小波变换滤波和Wiener滤波方法.
Support vector machine (SVM) is always researched and developed as a machine learning method on the base of statistical learning theory.As viewed from signal and system,the least squares support vector machine (LS-SVM) with the translation invariant kernel is a linear time invariant system.Taking the Ricker wavelet kernel as an example,we investigate the effects of different parameters on frequency responses of the least squares support vector regression (LS-SVR) filter.Those parameters affect the rising edge,the band width and central frequency of passband,and also the attenuation of signal energy.In other words,the longer the length of LS-SVR filter,the sharper the rising edge generated;the larger the kernel parameter,the higher the central frequency and the wider the bandwidth of the passband;the smaller the regularization parameter,the narrower the bandwidth of passband and the greater the attenuation of the desired signal.The experimental results of synthetic seismic data show that the LS-SVR filter with the Ricker wavelet kernel works better than the LS-SVR filter with the RBF kernel,the wavelet transform-based method and adaptive Wiener filtering method.
Support vector machine (SVM) is always researched and developed as a machine learning method on the base of statistical learning theory.As viewed from signal and system,the least squares support vector machine (LS-SVM) with the translation invariant kernel is a linear time invariant system.Taking the Ricker wavelet kernel as an example,we investigate the effects of different parameters on frequency responses of the least squares support vector regression (LS-SVR) filter.Those parameters affect the rising edge,the band width and central frequency of passband,and also the attenuation of signal energy.In other words,the longer the length of LS-SVR filter,the sharper the rising edge generated;the larger the kernel parameter,the higher the central frequency and the wider the bandwidth of the passband;the smaller the regularization parameter,the narrower the bandwidth of passband and the greater the attenuation of the desired signal.The experimental results of synthetic seismic data show that the LS-SVR filter with the Ricker wavelet kernel works better than the LS-SVR filter with the RBF kernel,the wavelet transform-based method and adaptive Wiener filtering method.
引文
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[3] Liu Y,Liu C,Wang D.A 1D time-varying median filter for seismic random,spike-like noise elimination.Geophysics,2009,74(1) :17～24
[4] 刘洋,Fomel Sergey,刘财等.高阶seislet变换及其在随机噪声消除中的应用.地球物理学报,2009,52(8) :2142～2151 Liu Y,Fomel Sergey,Liu C,et al.High order seislet transform and its application of random noise attenuation.Chinese J.Geophys.(in Chinese),2009,52(8) :2142～2151
[5] 张中杰.多分量地震资料的各向异性处理和解释方法.哈尔滨:黑龙江教育出版社,2002 Zhang Z J.Anisotropy Processing and Interpretation of Multicomponent Seismic Data.Harbin:Heilongjiang Educational Press,2002
[6] Zhang Z J,Wang G J,Teng J W,et al.CDP mapping to obtain the fine structure of the crust and upper mantle from seismic sounding data:An example for the southeastern China.Phy.Earth Plant.Interiors,2000,122:133～146
[7] Vapnik V N.The Nature of Statistical Learning Theory.New York:Springer-Verlag,1995
[8] Li D L.Support vector regression based image denoising.Image and Vision Computing,2009,27:623～627
[9] Wu D X,Peng D Q,Tian J W.Image denoising using local adaptive least squares support vector regression.Geo-Spatial Information Science,2007,10(3) :196～199
[10] 邓小英,杨顶辉,刘 涛等.Ricker子波核支持向量回归的Mercer条件拓展问题研究.地球物理学报,2009,52(9) :2335～2344 Deng X Y,Yang D H,Liu T,et al.Study on Mercer condition extension of support vector regression based on Ricker wavelet kernel.Chinese J.Geophys.(in Chinese),2009,52(9) :2335～2344
[11] Cheng H,Tian J W,Liu J,et al.Wavelet domain image denoising via support vector regression.Electronics Letters,2004,40(23) :1479～1480
[12] Mercer J.Functions of positive and negative type and their connection with the theory of integral equations.Philosophical Transactions of the Royal Society of London(Series A),1909,209:415～446
[13] Smola A J,Sch(o|¨)lkopf B,M(u|¨)ller K-R.General cost functions for support vector regression.Proc.of the 8~(th)Int.Conf.Artificial Neural Networks,Australian,1998． 79～83
[14] Cherkassky V,Ma Y Q.Practical selection of SVM parameters and noise estimation for SVM regression.Neural Networks,2004,17:113～126
[15] The Math Works Inc.MATLAB,The language of Technical Computing.Version 7． 0． 0． 19920(R14) ,2004
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