Abstract
Inspired by the theory of multiresolution analysis (MRA) of wavelets and artificial neural networks, a multiresolution neural network (MRNN) for approximating arbitrary nonlinear functions is proposed in this paper. MRNN consists of a scaling function neural network (SNN) and a set of sub-wavelet neural networks, in which each sub-neural network can capture the specific approximation behavior (global and local) at different resolution of the approximated function. The structure of MRNN has explicit physical meaning, which indeed embodies the spirit of multiresolution analysis of wavelets. A hierarchical construction algorithm is designed to gradually approximate unknown complex nonlinear relationship between input data and output data from coarse resolution to fine resolution. Furthermore, A new algorithm based on immune particle swarm optimization (IPSO) is proposed to train MRNN. To illustrate the effectiveness of our proposed MRNN, experiments are carried out with different kinds of wavelets from orthonormal wavelets to prewavelets. Simulation results show that MRNN provides accurate approximation and good generalization.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zhang, Q.H., Benveniste, A.: Wavelet networks. IEEE Trans. Neural Netw. 3(6), 889–898 (1992)
Pati, Y.C., Krishnaprasad, P.S.: Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformation. IEEE Trans. Neural Networks 4, 73–85 (1993)
Zhang, J., Walter, G.G., Lee, W.N.W.: Wavelet neural networks for function learning. IEEE Trans. Signal Processing 43, 1485–1497 (1995)
Zhang, Q.: Using wavelet networks in nonparametric estimation. IEEE Trans. Neural Networks 8, 227–236 (1997); Beijing, P.R. China, pp. 451–456 (June 1999)
Alonge, F., Dippolito, F., Mantione, S., Raimondi, F.M.: A new method for optimal synthesis of wavelet-based neural networks suitable for identification purposes. In: Proc. 14th IFAC, Beijing, P.R. China, June 1999, pp. 445–450 (1999)
Li, X., Wang, Z., Xu, L., Liu, J.: Combined construction of wavelet neural networks for nonlinear system modeling. In: Proc. 14th IFAC, Beijing, P.R. China, June 1999, pp. 451–456 (1999)
Chen, J., Bruns, D.D.: WaveARX neural network development for system identification using a systematic design synthesis. Ind. Eng. Chem. Res. 34, 4420–4435 (1995)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proc. 6th Int. Symp. Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)
Eberhart, R.C., Simpson, P., Dobbins, R.: Computational Intelligence PC Tools: Academic, ch. 6, pp. 212–226 (1996)
Eberhart, R.C., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization, Evolutionary Prograinniing VII. In: Proc. 71h Ann. Conf. on Evolutionary Prograriirnirig Conf., San Diego, CA, Springer, Berlin (1998)
Dusgupta, D.: Artificial Immnue Systems and their applications. Springer, Berlin Heidelberg (1999)
Chen, J., Bruns, D.D.: WaveARX neural network development for system identification using a systematic design synthesis. Ind. Eng. Chem. Res. 34, 4420–4435 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ying, L., Zhidong, D. (2006). Multiresolution Neural Networks Based on Immune Particle Swarm Algorithm. In: Jiao, L., Wang, L., Gao, Xb., Liu, J., Wu, F. (eds) Advances in Natural Computation. ICNC 2006. Lecture Notes in Computer Science, vol 4221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881070_16
Download citation
DOI: https://doi.org/10.1007/11881070_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45901-9
Online ISBN: 978-3-540-45902-6
eBook Packages: Computer ScienceComputer Science (R0)