Abstract
The kernel function of support vector machine (SVM) is an important factor for the learning result of SVM. Based on the wavelet decomposition and conditions of the support vector kernel function, Littlewood-Paley wavelet kernel function for SVM is proposed. This function is a kind of orthonormal function, and it can simulate almost any curve in quadratic continuous integral space, thus it enhances the generalization ability of the SVM. According to the wavelet kernel function and the regularization theory, Least squares Littlewood-Paley wavelet support vector machine (LS-LPWSVM) is proposed to simplify the process of LPWSVM. The LS-LPWSVM is then applied to the regression analysis and classifying. Experiment results show that the precision is improved by LS-LPWSVM, compared with LS-SVM whose kernel function is Gauss function.
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
Vapnik, V.: The Nature of Statistical Learning Theory, pp. 1–175. Springer, New York (1995)
Zhang, X.G.: Introduction to Statistical Learning Therory and Support Vector Machines. Acta Automatica Snica 26(1), 32–42 (2000)
Burges, C.J.C.: A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2(2), 955–974 (1998)
Bernhard, S., Sung, K.K.: Comparing Support Vector Machines with Gaussian Kernels to Radical Basis Fuction Classifiers. IEEE Transaction on Signal Processing 45(11), 2758–2765 (1997)
Edgar, O., Robert, F., Federico, G.: Training Support Vector Machines: An Application to Face Detection. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 130–136 (1997)
Mercer, J.: Function of positive and negative type and their connection with the theory of integral equations. Philosophical Transactions of the Royal Society of London: A 209, 415–446 (1909)
Stein, E.M.: Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Princeton University Press and the University of Tokio Press, Princeton (1970)
Suykens, J.A.K., Vandewalle, J.: Least squares support vector machine classifiers. Neural Processing Letter 9(3), 293–300 (1999)
Burges, C.J.C.: Geometry and invariance in kernel based methods. In: Advance in Kernel Methods-Support Vector Learning, pp. 89–116. MIT Press, Cambridge (1999)
Smola, A., Schölkopf, B., Müller, K.R.: The connection between regularization operators and support vector kernels. Neural Networks 11(4), 637–649 (1998)
Zhang, Q., Benveniste, A.: Wavelet networks. IEEE Trans on Neural Networks 3(6), 889–898 (1992)
ftp://ftp.ics.uci.edu.cn/pub/machine-learning-database/adult
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
Wu, F., Zhao, Y. (2005). Least Squares Littlewood-Paley Wavelet Support Vector Machine. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_47
Download citation
DOI: https://doi.org/10.1007/11579427_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29896-0
Online ISBN: 978-3-540-31653-4
eBook Packages: Computer ScienceComputer Science (R0)