A novel online adaptive kernel method with kernel centers determined by a support vector regression approach

The optimality of the kernel number and kernel centers plays a significant role in determining the approximation power of nearly all kernel methods. However, the process of choosing optimal kernels is always formulated as a global optimization task, which is hard to accomplish. Recently, an improved algorithm called recursive reduced least squares support vector regression (IRR-LSSVR) was proposed for establishing a global nonparametric offline model. IRR-LSSVR demonstrates a significant advantage in choosing representing support vectors compared with others. Inspired by the IRR-LSSVR, a new online adaptive parametric kernel method called Weights Varying Least Squares Support Vector Regression (WV-LSSVR) is proposed in this paper using the same type of kernels and the same centers as those used in the IRR-LSSVR. Furthermore, inspired by the multikernel semiparametric support vector regression, the effect of the kernel extension is investigated in a recursive regression framework, and a recursive kernel method called Gaussian Process Kernel Least Squares Support Vector Regression (GPK-LSSVR) is proposed using a compound kernel type which is recommended for Gaussian process regression. Numerical experiments on benchmark data sets confirm the validity and effectiveness of the presented algorithms. The WV-LSSVR algorithm shows higher approximation accuracy than the recursive parametric kernel method using the centers calculated by the k-means clustering approach. The extended recursive kernel method (i.e. GPK-LSSVR) has not shown any advantage in terms of global approximation accuracy when validating the test data set without real-time updates, but it can increase modeling accuracy if real-time identification is involved.