Abstract
Lowe [1] proposed that the kernel parameters of a radial basis function (RBF) neural network may first be fixed and the weights of the output layer can then be determined by pseudo-inverse. Jang, Sun, and Mizutani (p.342 [2]) pointed out that this type of two-step training methods can also be used in fuzzy neural networks (FNNs). By extensive computer simulations, we [3] demonstrated that an FNN with randomly fixed membership function parameters (FNN-RM) has faster training and better generalization in comparison to the classical FNN. To provide a theoretical basis for the FNN-RM, we present an intuitive proof of the universal approximation ability of the FNN-RM in this paper, based on the orthogonal set theory proposed by Kaminski and Strumillo for RBF neural networks [4].
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Wang, L., Liu, B., Wan, C. (2005). On the Universal Approximation Theorem of Fuzzy Neural Networks with Random Membership Function Parameters. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_6
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DOI: https://doi.org/10.1007/11427391_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
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