Extending the functional training approach for B-splines

Cristiano L. Cabrita, António E. Ruano, Pedro M. Ferreira, László T. Kóczy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication2012 International Joint Conference on Neural Networks, IJCNN 2012
DOIs
Publication statusPublished - Aug 22 2012
Event2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012 - Brisbane, QLD, Australia
Duration: Jun 10 2012Jun 15 2012

Publication series

NameProceedings of the International Joint Conference on Neural Networks

Other

Other2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012
CountryAustralia
CityBrisbane, QLD
Period6/10/126/15/12

Keywords

  • Levenberg-Marquardt algorithm
  • Neural networks training
  • functional training
  • parameter separability

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

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  • Cite this

    Cabrita, C. L., Ruano, A. E., Ferreira, P. M., & Kóczy, L. T. (2012). Extending the functional training approach for B-splines. In 2012 International Joint Conference on Neural Networks, IJCNN 2012 [6252741] (Proceedings of the International Joint Conference on Neural Networks). https://doi.org/10.1109/IJCNN.2012.6252741