Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification

Wavelet theory has a profound impact on signal processing as it offers a rigorous mathematical framework to the treatment of multiresolution problems. The combination of soft computing and wavelet theory has led to a number of new techniques. On the other hand, as a new generation of learning algorithms, support vector regression (SVR) was developed by Vapnik et al. recently, in which ϵ-insensitive loss function was defined as a trade-off between the robust loss function of Huber and one that enables sparsity within the SVs. The use of support vector kernel expansion also provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, for the support vector regression with the standard quadratic programming technique, the implementation is computationally expensive and sufficient model sparsity cannot be guaranteed. In this article, from the perspective of model sparsity, the linear programming support vector regression (LP-SVR) with wavelet kernel was proposed, and the connection between LP-SVR with wavelet kernel and wavelet networks was analyzed. In particular, the potential of the LP-SVR for nonlinear dynamical system identification was investigated.