Abstract
Based on the wavelet decomposition and reproducing kernel Hilbert space (RKHS), a novel notion of least squares wavelet support vector machine (LS-WSVM) with universal reproducing wavelet kernels is proposed for approximating arbitrary nonlinear functions. The good reproducing property of wavelet kernel function enhances the generalization ability of LS-WSVM method and some experimental results are presented to illustrate the feasibility of the proposed method.
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
Qinghua, Z., Benvenisite, A.: Wavelet networks. IEEE Tran. on neural Network 3(6), 889–898 (1992)
Qinghua, Z.: Using wavelet networks in nonparametric estimation. IEEE Tran. on Neural Network 8(2), 227–236 (1997)
Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (1998)
Vapnik, V., Golowich, S., Smola, A.: Support vector method for function approximation, regression estimation, and signal processing. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9, pp. 281–287. MIT Press, Cambridge (1997)
Rakotomamonjy, A., Mary, X., Canu, S.: Wavelet Kernel in RKHS. In: Proc. of Statistical Learning: Theory and Applications, Paris (2002)
Li, Z., Weida, Z., Licheng, J.: Wavelet Support Vector Machine. IEEE Transactions on Systems, Man, And Cybernetics—Part B: Cybernetics 34(1), 34–39 (2004)
Mercer, J.: Functions of positive and negative type and their connection with the theory of integral equations. Transactions of the London Philosophical Society A 209, 415–446 (1909)
Aronszajn, N.: Theory of reproducing kernels. Transactions of the American Society 68, 337–404 (1950)
Daubechies, I.: Ten lectures on wavelets. In: CBMS-NSF conference series in applied mathematics, vol. 137(152), pp. 117–119. SIAM, Philadelphia (1992)
Mallat, S.: A wavelet tour of signal processing, 2nd edn. Academic Press, London (2003)
Canu, S., Mary, X., Rakotomamonjy, A.: Functional learning through kernel. In: Suykens, J., Horvath, G., Basu, S., Micchelli, C., Vandewalle, J. (eds.) Advances in Learning Theory: Methods, Models and Applications. NATO Science Series III: Computer and Systems Sciences, vol. 190, pp. 89–110. IOS Press, Amsterdam (2003)
Narendra, K., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE tran. on Neural Network. 1(1), 4–27 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wen, X., Xu, X., Cai, Y. (2005). Least-Squares Wavelet Kernel Method for Regression Estimation. In: Wang, L., Chen, K., Ong, Y.S. (eds) Advances in Natural Computation. ICNC 2005. Lecture Notes in Computer Science, vol 3610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539087_74
Download citation
DOI: https://doi.org/10.1007/11539087_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28323-2
Online ISBN: 978-3-540-31853-8
eBook Packages: Computer ScienceComputer Science (R0)