最小二乘支持向量回归滤波系统性能分析

Performance analysis of least squares support vector regression filtering system

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.