Abstract
A new weighted wavelet neural network is presented, And the approximation capability of such weighted wavelet neural network is also studied based on the traits of Lebesgue partition, the operator theory and the topology structure of the relatively compact set in Hilbert space. The simulation results indicate that the weighted wavelet neural network is a uniformed approximator, which can approximates the nonlinear function in compact set by arbitrary precision.
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References
Funahashi, K.: On the Approximate Realization of Continuous Mappings by Neural Networks. Neural Networks 1, 183–192 (1989)
Cybenko, G.: Approximation by Superpositions of a Sigmoidal Function. Mathematics of Control, Signals and Systems 1, 303–314 (1989)
Hornik, K.: Approximation Capabilities of Multiplayer Feedforward Networks. Neural networks 1, 251–257 (1991)
Pati, Y.C., Krishnaprasad, P.S.: Discrete Affine Wavelet Transforms for Analysis and Synthesis of Feedforward Neural Networks. Advances in Neural Information Processing Systems 1, 743–749 (1991)
Zhang, Q.H., Benveniste, A.: Wavelet Networks. IEEE Trans. Neural Networks 1, 889–898 (1992)
Zhang, Q.H.: Using Wavelet Network in Nonparametric Estimation. IEEE Trans. Neural Networks 1, 227–236 (1997)
Oussar, Y., Rivals, I., Personnaz, L., Dreyfus, G.: Training Wavelet Networks for Nonlinear Dynamic Input-output Modeling. Neurocomputing 1, 173–188 (1998)
Xu, J.X., Tan, Y.: Nonlinear Adaptive Wavelet Control Using Constructive Wavelet Networks. In: Proceeding of American Control Conference, Arlington, VA (2001)
Parasuraman, K., Elshorbagy, A.: Wavelet Networks: An Alternative to Classical Neural Networks. In: Proceedings of International Joint Conference on Neural Networks, Montreal, Canada (2005)
Tang, X.Y., Zhang, Y.L.: Pattern Recognition for Fault Based on BP Wavelet Network. Computer Engineering 1, 94–96 (2003)
Daubechies, I.: Orthonormal Bases of Compactly Supported Wavelets. Comm. Pure. Appl. Math. 1, 909–996 (1988)
Chui, C.K., Wang, J.Z.: A General Framework of Compactly Supported Splines and Wavelets. J. Approx. Theory 1, 263–304 (1992)
Krishnaswami, A.: A Fundamental Invariant in the Theory of Partitions. Topics in Number Theory. Kluwer. Acad. Publ, Dordrecht (1999)
Bartsch, R.: Ascoli-Arzela-theory Based on Continuous Convergence in an (almost) Non-Hausdorff Setting. Categorical Topology 1, 221–240 (1996)
Ying, H.: Sufficient Conditions on Uniform Approximation of Multivariate Functions by General Takagi-Sugeno Fuzzy Systems with Linear Rule Consequent. IEEE Trans. Sys., Man. and Cyber. 1, 515–520 (1998)
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Hu, SS., Hou, X., Zhang, JF. (2007). Approximation Property of Weighted Wavelet Neural Networks. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_145
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DOI: https://doi.org/10.1007/978-3-540-72383-7_145
Publisher Name: Springer, Berlin, Heidelberg
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