Abstract
In order to resolve the noise reduction in chaotic time series, a novel method based on Multi-dimensional version of Recurrent Least Square Support Vector Machine(MDRLS-SVM) is proposed in this paper. By analyzing the relationship between the function approximation and the noise reduction, we realized that the noise reduction can be implemented by the function approximation techniques. On the basis of the MDRLS-SVM and the reconstructed embedding phase theory, the function approximation in the high dimensional embedding phase space is carried out and the noise reduction achieved simultaneously.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Schreiber, T., Grassberger, P.: A simple noise-reduction method for real data. Phys. Lett. A 160, 411–418 (1991)
Cawley, R., Hsu, G.H.: Local-geometric-projection method for noise reduction in chaotic maps and flows. Phys. Rev. A 46, 3057–3082 (1992)
Kantz, H., Schreiber, T., Hoffmann, I., Buzug, T., Pfister, G., Flepp, L.G., Simonet, J., Badii, R., Brun, E.: Nonlinear noise reduction: A case study on experimental data. Phys. Rev. E 48, 1529–1538 (1993)
Leontitsis, A., Bountis, T., Pagge, J.: An adaptive way for improving noise reduction using Local Geometric Projection. CHAOS 14(1), 106–110 (2004)
Farmer, J.D., Sidorowich, J.J.: Optimal shadowing and noise reduction. Physica D 47, 373–392 (1991)
Davies, M.E.: Noise reduction schemes for chaotic time series. Physica D 79, 174–192 (1994)
Kern, A., Steeb, W.H., Stoop, R.: Projective noise cleaning with dynamic neighborhood selection. Int. J. Mod. Phys. C 11, 125–146 (2000)
Suykens, J.A.K., Vandewalle, J.: Recurrent Least Squares Support Vector Machines. IEEE Tran. on Circuits and System-I: Fundamental Theory and Applications 47(7), 1109–1114 (2000)
Takens, F.: Detecting strange attractors in fluid turbulence. In: Rand, D., Young, L.S. (eds.) Dynamical systems and turbulence, pp. 366–381. Springer, Heidelberg (1981)
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
Sun, J., Zhou, Y., Bai, Y., Luo, J. (2006). Nonlinear Noise Reduction of Chaotic Time Series Based on Multi-dimensional Recurrent Least Squares Support Vector Machines. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_100
Download citation
DOI: https://doi.org/10.1007/11893028_100
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46479-2
Online ISBN: 978-3-540-46480-8
eBook Packages: Computer ScienceComputer Science (R0)