Abstract—An algorithm for constructing and training the Dyadic Wavelet Neural Network is proposed combining the theory of multiresolution analysis (MRA) of wavelet transforms and the conventional neural networks. The focus is to mainly improve function approximation accuracy in terms of dilation and translation parameters of wavelets, meanwhile not increasing the number of wavelet bases leading to optimal network structure. The proposed activation functions are drawn from a family of orthonormal basis functions. The good localization characteristics of the basis functions, both in the input and frequency domain allow hierarchical, multi-resolution learning of input-output function from experimental data. Compared with Wavelet Neural Networks of previous works, the model accuracy and generalization capability of the DWN are improved by adjusting the resolution parameter as it plays a significant role in dyadic wavelet analysis and approximation of a given function. In the learning process exhaustive experimentations are conducted to illustrate the impact of learning rate with respect to the generalization of the output function. All these advantages have been reflected in our experimentations. Two benchmark functions are simulated to illustrate the effectiveness of the method.
Index Terms—Dyadic Wavelet Neural Networks (DWN), Function learning, Orthonormal scaling functions, Wavelet Transforms (WT).
M. P. Pushpalatha is with Department of Computer Science and Engineering Sri Jayachamarajendra College of Engineering Mysore -570006, India (phone: 091 821-2548285; fax: 091 821-2548280; e-mail: mppvin@gmail.com.)
Nalini N. is with Department of Computer Science and Engineering, Nitte Meenakshi Institute of Technology, Bangalore, India. (email: nalinaniranjan@hotmail.com).
Cite: Pushpalatha M. P. and Nalini N, "Comparative Analysis of the Generalization of Dyadic Wavelet based Neural Networks (DWNN) towards Optimal Network Structure for Non-linear Function Estimation," International Journal of Computer Theory and Engineering vol. 3, no. 1, pp. 163-170, 2011.
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