Performance analysis of least squares support vector regression filtering system

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.