Regularized Least Squares Twin SVR for the Simultaneous Learning of a Function and its Derivative

In a recent publication, Lazaro et al. addressed the problem of simultaneously approximating a function and its derivative using support vector machines. In this paper, we propose a new approach termed as regularized least squares twin support vector regression, for the simultaneous learning of a function and its derivatives. The regressor is obtained by solving one of two related support vector machine-type problems, each of which is of a smaller size than the one obtained in Lazaro's approach. The proposed algorithm is simple and fast, as no quadratic programming problem needs to be solved. Effectively, only the solution of a pair of linear systems of equations is needed.