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Publication
Exploiting the functional training approach in B-Splines
Advisor(s)
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. These later terms can be numerically computed with the data.
The use of the functional approach is introduced here for B-splines. An example shows that, besides great computational complexity savings, this approach obtains better results than the standard, discrete
technique, as the performance surface employed is more similar to the one obtained with the function underlying the data. In some cases, as shown in the example, a complete analytical solution can be found.
Description
Keywords
Neural networks training Parameter separability Functional back-propagation
Citation
Ruano, A. E.; Cabrita, C.; Ferreira, P. M.; Koczy, L. T. Exploiting the Functional Training Approach in B-Splines, Trabalho apresentado em Embedded Systems, Computational Intelligence and Telematics in Control, In Proceedings of the 1st Conference on Embedded Systems, Computational Intelligence and Telematics in Control, Wurzburg, 2012.