Nonlinear system identification based on SVR with quasi-linear kernel

In recent years, support vector regression (SVR) has attracted much attention for nonlinear system identification. It can solve nonlinear problems in the form of linear expressions within the linearly transformed space. Commonly, the convenient kernel trick is applied, which leads to implicit nonlinear mapping by replacing the inner product with a positive definite kernel function. However, only a limited number of kernel functions have been found to work well for the real applications. Moreover, it has been pointed that the implicit nonlinear kernel mapping is not always good, since it may faces the potential over-fitting for some complex and noised learning task. In this paper, explicit nonlinear mapping is learnt by means of the quasi-ARX modeling, and the associated inner product kernel, which is named quasi-linear kernel, is formulated with nonlinearity tunable between the linear and nonlinear kernel functions. Numerical and real systems are simulated to show effectiveness of the quasi-linear kernel, and the proposed identification method is also applied to microarray missing value imputation problem.