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Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

Hong, X. and Harris, C.J. (2000) Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition. IEEE Transactions on Neural Networks, 11 (4). pp. 889-902. ISSN 1045-9227

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To link to this article DOI: 10.1109/72.857770

Abstract/Summary

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Systems Engineering
ID Code:18505
Uncontrolled Keywords:Delaunay input space partition, RBF networks, additive decomposition, additive decomposition construction, basis function nonnegativity, bivariate Bezier-Bernstein polynomial functions, curse of dimensionality, fuzzy membership functions, fuzzy networks, generalized neurofuzzy network modeling algorithms, interpretability, multidimensional inputs, nonlinear dynamic systems, structural parsimony, univariate Bezier-Bernstein polynomial functions
Publisher:IEEE

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