Non-Mercer hybrid kernel for linear programming support vector regression in nonlinear systems identification

As a new sparse kernelmodelingmethod, support vector regression (SVR) has been regarded as the stateof-the-art technique for regression and approximation. In [V.N. Vapnik, The Nature of Statistical Learning Theory, second ed., Springer-Verlag, 2000], Vapnik developed the e-insensitive loss function for the support vector regression as a trade-off between the robust loss function of Huber and one that enables sparsity within the support vectors. The use of support vector kernel expansion provides us a potentia avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, in the standard quadratic programming support vector regression (QP-SVR), its implementation is often computationally expensive and sufficientmodel sparsity cannot be guaranteed. In an attempt tomitigate these drawbacks, this article focuses on the application of the soft-constrained linear programming support vector regression (LP-SVR) with hybrid kernel in nonlinear black-box systems identification. An innovative non-Mercer hybrid kernel is explored by leveraging the flexibility of LP-SVR in choosing the kernel functions. The simulation results demonstrate the ability to use more general kernel function and the inherent performance advantage of LP-SVR to QP-SVR in terms of model sparsity and computationa efficiency. 2008 Elsevier B.V. All rights reserved