Abstract
Kernel-based machine learning techniques, such as support vector machines, regularization networks, have been widely used in pattern analysis. Kernel function plays an important role in the design of such learning machines. The choice of an appropriate kernel is critical in order to obtain good performance. This paper presents a new class of kernel functions derived from framelet. Framelet is a wavelet frame constructed via multiresolution analysis, and has both the merit of frame and wavelet. The usefulness of the new kernels is demonstrated through simulation experiments.
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
Poggio, T., Girosi, F.: Networks for approximation and learning. Proc. IEEE 78(9), 1481–1497 (1990)
Bertero, M., Poggio, T., Torre, V.: Ill-posed problems in early vision. Proc. IEEE 76, 869–889 (1988)
Chapelle, O., et al.: Choosing multiple parameters for support vector machines. Machine Learning 46, 131–159 (2002)
Cortes, C., Vapnik, V.N.: Support vector networks. Machine Learning 20, 1–25 (1995)
Cuker, F., Smale, S.: Best choices for regularization parameters in learning theory: on the bias-variance problem. Found. Comput. Math. 2, 413–428 (2002)
Daubechies, I., et al.: Framelets: MRA-based constructions of wavelet frames. Appl. Comput. Harmon. Anal. 124, 44–88 (2003)
Evgeniou, T., Pontil, M., Poggio, T.: Regularization networks and support vector machines. Advances in Computational Mathematics 13, 1–50 (2000)
Gao, J.B., Harris, C.J., Gunn, S.R.: On a class of support vector kernels based on frames in function hilbert spaces. Neural Computation 13(9), 1975–1994 (2001)
Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Comput. 7, 219–269 (1995)
Müller, K.R., et al.: An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)
Rakotomamonjy, A., Mary, X., Canu, S.: Non-parametric regression with wavelet kernels. Appl. Stochastic Models Bus. Ind. 21, 153–163 (2005)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge Univ. Press, Cambridge (2004)
Smola, A.J., Schölkopf, B., Müller, K.R.: The connection between regularization operators and support vector kernels. Neural Networks 11, 637–649 (1998)
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-posed Problems. W.H. Winston, Washington (1977)
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
Zhang, L., Zhou, W., Jiao, L.: Wavelet support vector machine. IEEE T. on System, Man and Cybernetics-Part B: Cybernetics 34(1), 34–39 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Zhang, WF., Dai, DQ., Yan, H. (2007). On a New Class of Framelet Kernels for Support Vector Regression and Regularization Networks. In: Zhou, ZH., Li, H., Yang, Q. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2007. Lecture Notes in Computer Science(), vol 4426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71701-0_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-71701-0_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71700-3
Online ISBN: 978-3-540-71701-0
eBook Packages: Computer ScienceComputer Science (R0)