Extending the functional training approach for B-splines

Cabrita, Cristiano Lourenço; Ruano, Antonio; Ferreira, P. M.; Kóczy, László T.

http://hdl.handle.net/10400.1/2130

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Authors

Cabrita, Cristiano Lourenço

Ruano, Antonio

Ferreira, P. M.

Kóczy, László T.

Abstract(s)

When used for function approximation purposes, neural networks belong to a class of models whose parameters can be separated into linear and nonlinear, according to their influence in the model output. This concept of parameter separability can also be applied when the training problem is formulated as the minimization of the integral of the (functional) squared error, over the input domain. Using this approach, the computation of the gradient involves terms that are dependent only on the model and the input domain, and terms which are the projection of the target function on the basis functions and on their derivatives with respect to the nonlinear parameters, over the input domain. This paper extends the application of this formulation to B-splines, describing how the Levenberg- Marquardt method can be applied using this methodology. Simulation examples show that the use of the functional approach obtains important savings in computational complexity and a better approximation over the whole input domain.

Keywords

Neural networks training Parameter separability Functional training Levenberg-Marquardt algorithm

URI

http://hdl.handle.net/10400.1/2130

Citation

Cabrita, Cristiano L.; Ruano, Antonio E.; Ferreira, Pedro M.; Koczy, Laszlo T. Extending the functional training approach for B-splines, Trabalho apresentado em 2012 International Joint Conference on Neural Networks (IJCNN 2012 - Brisbane), In Proceedings of the 2012 International Joint Conference on Neural Networks (IJCNN), Brisbane, Australia, 2012.