Abstract
This paper deals with a way of constructing reproducing kernel Hilbert spaces and their associated kernels from frame theory. After introducing briefly frame theory, we give mild conditions on frame elements for spanning a RKHS. Examples of different kernels are then given based on wavelet frame. Thus, issues of this way of building kernel for semiparametric learning are discussed and an application example on a toy problem is described.
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
N. Cristianini and J. Shawe-Taylor. Introduction to Support Vector Machines. Cam-bridge University Press, 2000.
I. Daubechies. Ten Lectures on Wavelet. SIAM, CBMS-NSF regional conferences edition, 1992.
R. Duffin and A. Schaeffer. A class of nonharmonic fourier series. Trans. Amer. Math. Soc., 72:341–366, 1952.
T. Evgeniou, M. Pontil, and T. Poggio. Regularization networks and support vector machines. Advances in Computational Mathematics, 13(1):1–50, 2000.
J. Gao, C. Harris, and S. Gunn. On a class of a support vector kernels based on frames in function hilbert spaces. Neural Computation, 13(9):1975–1994, 2001.
K. Grochenig. Acceleration of the frame algorithm. IEEE Trans. Signal Proc. 41(12):3331–3340, 1993.
G. Kimeldorf and G. Wahba. Some results on Tchebycheffian spline functions. J. Math. Anal. Applic., 33:82–95, 1971.
S. Mallat. A wavelet tour of signal processing. Academic Press, 1998.
A. Rakotomamonjy and S. Canu. Learning, frame, reproducing kernel and regularization. Technical Report TR2002-01, Perception, Systèmes et Information, INSA de Rouen, 2002.
B. Schölkopf, P. Y. Simard, A. J. Smola, and V. Vapnik. Prior knowledge in support vector kernels. In M. I. Jordan, M. J. Kearns, and S. A. Solla, editors, Advances in Neural information processings systems, volume 10, pages 640–646, Cambridge, MA, 1998. MIT Press.
A. Smola. Learning with Kernels. PhD thesis, Published by: GMD, Birlinghoven, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rakotomamonjy, A., Canu, S. (2002). Frame Kernels for Learning. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_115
Download citation
DOI: https://doi.org/10.1007/3-540-46084-5_115
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44074-1
Online ISBN: 978-3-540-46084-8
eBook Packages: Springer Book Archive