Abstract
The SVM has been used to the nonlinear function mapping successfully, but the universal approximation property of the SVM has never been proved in theory. This paper proves the universal approximation of the SVM with RBF kernel to arbitrary functions on a compact set and deduces it to the approximation of discrete function. From simulation we can see that the RBF kernel based LS-SVM is more effective in nonlinear function estimation and can prevent the system from noise pollution, so it has high generalization ability.
Supported by a grant from the National High Technology Research and Development Program of China (863 Program) (No. 2003AA501100) and China Postdoctoral Science Foundation (No.2003034145).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Suykens, J.A.K.: Nonlinear Modeling and Support Vector Machines. In: IEEE Conference on Instrumentation and Measurement Technology, Budapest, Hungary, May, pp. 287–294 (2001)
Suykens, J.A.K.: Sparse Approximation Using Least Squares Support Vector Machines. In: IEEE Int. Symposium on Circuit and Systems, Geneva, Switzerland, May, pp. 757–760 (2000)
Rui, F.: Soft Sensor Modeling Based on Support Vector Machine. Information and Control 31(6), 567–571 (2002)
Wang, J.P., Jing, Z.L.: A Stochastic Fuzzy Neural Network with Universal Approximation and Its Application. In: Proc. of Int. Conf. On Fuzzy Information Processing Theories and Applications, pp. 497–502. Tsinghua University Press & Springer, Beijing (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, J., Chen, Q., Chen, Y. (2004). RBF Kernel Based Support Vector Machine with Universal Approximation and Its Application. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_85
Download citation
DOI: https://doi.org/10.1007/978-3-540-28647-9_85
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22841-7
Online ISBN: 978-3-540-28647-9
eBook Packages: Springer Book Archive