Surface Modelling with Radial Basis Functions Neural Networks Using Virtual Environments
Modelling capabilities of Radial Basis Function Neural Networks (RBFNNs) are very dependent on four main factors: the number of neurons, the central location of each neuron, their associated weights and their widths (radii). In order to model surfaces defined, for example, as y = f(x,z), it is common to use tri-dimensional gaussian functions with centres in the (X,Z) domain. In this scenario, it is very useful to have visual environments where the user can interact with every radial basis function, modify them, inserting and removing them, thus visually attaining an initial configuration as similar as possible to the surface to be approximated. In this way, the user (the novice researcher) can learn how every factor affects the approximation capability of the network, thus gaining important knowledge about how algorithms proposed in the literature tend to improve the approximation accuracy. This paper presents a didactic tool we have developed to facilitate the understanding of surface modelling concepts with ANNs in general and of RBFNNs in particular, with the aid of a virtual environment.
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- 1.Chen, S.: Orthogonal Least Squares Learning for Radial Basis Function Networks. IEEE Transactions on Neural Network 2(2) (1991)Google Scholar
- 2.Duda, R.O., Hart, P.E.: Pattern Classification and Scene Systems. Wiley, New York (1973)Google Scholar
- 3.González, J., Rojas, I., Pomares, H., Ortega, J., Prieto, A.: A New Clustering Technique for Function Approximation. IEEE Transactions on Neural Networks 13(1) (2002)Google Scholar
- 5.Haykin, S.: Neural Networks a comprehensive foundation, 2nd edn. Prentice Hall, Englewood Cliffs (1998)Google Scholar
- 6.Loewe, D.: Adaptative Radial Basis Function Nonlinearities, and the Problem of Generalisation. In: First IEEE International Conference on Artificial Neural Networks, London, pp. 171–175 (1989)Google Scholar
- 10.Benoudjit, N., Archambeau, C., Lendasse, A., Lee, J., Verleysen, M.: Width optimization of the Gaussian kernels in Radial Basis Function Networks. In: Proceedings of ESANN, April 2002, pp. 425–432 (2002)Google Scholar