Partially linear models and least squares support vector machines

Within the context of nonlinear system identification, the LS-SVM formulation is extended to define a partially linear LS-SVM in order to identify a model containing a linear part and a nonlinear component. For a given kernel, a unique solution exists when the parametric part has full column rank, although identifiability problems can arise for certain structures. The solution has close links with traditional semiparametric techniques from the statistical literature. The properties of the model are illustrated by Monte Carlo simulations over different structures, and iterative forecasting examples for Hammerstein and other systems show a good global performance and an accurate identification of the linear part.