Abstract
The role of width in kernel models and radial-basis function networks is investigated with a special emphasis on the Gaussian case. Quantitative bounds are given on kernel-based regularization showing the effect of changing the width. These bounds are shown to be d-th powers of width ratios, and so they are exponential in the dimension of input data.
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
Fine, T.L.: Feedforward Neural Network Methodology. Springer, Heidelberg (1999)
Kecman, V.: Learning and Soft Computing. MIT Press, Cambridge (2001)
Park, J., Sandberg, I.: Universal approximation using radial–basis–function networks. Neural Computation 3, 246–257 (1991)
Park, J., Sandberg, I.: Approximation and radial basis function networks. Neural Computation 5, 305–316 (1993)
Mhaskar, H.N.: Versatile Gaussian networks. In: Proceedings of IEEE Workshop of Nonlinear Image Processing, pp. 70–73 (1995)
Kainen, P.C., Kůrková, V., Sanguineti, M.: Complexity of Gaussian radial basis networks approximating smooth functions. J. of Complexity 25, 63–74 (2009)
Cucker, F., Smale, S.: On the mathematical foundations of learning. Bulletin of AMS 39, 1–49 (2002)
Poggio, T., Smale, S.: The mathematics of learning: dealing with data. Notices of AMS 50, 537–544 (2003)
Kůrková, V.: Neural network learning as an inverse problem. Logic Journal of IGPL 13, 551–559 (2005)
Gribonval, R., Vandergheynst, P.: On the exponential convergence of matching pursuits in quasi-incoherent dictionaries. IEEE Trans. on Information Theory 52, 255–261 (2006)
Aronszajn, N.: Theory of reproducing kernels. Transactions of AMS 68, 337–404 (1950)
Strichartz, R.: A Guide to Distribution Theory and Fourier Transforms. World Scientific, NJ (2003)
Loustau, S.: Aggregation of SVM classifiers using Sobolev spaces. Journal of Machine Learning Research 9, 1559–1582 (2008)
Girosi, F.: An equivalence between sparse approximation and support vector machines. Neural Computation (AI memo 1606) 10, 1455–1480 (1998)
Girosi, F., Poggio, T.: Regularization algorithms for learning that are equivalent to multilayer networks. Science 247(4945), 978–982 (1990)
Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Computation 7, 219–269 (1995)
Kůrková, V.: Learning from data as an inverse problem in reproducing kernel Hilbert spaces. Inverse Problems in Science and Engineering (2010) (submitted)
Wahba, G.: Splines Models for Observational Data. SIAM, Philadelphia (1990)
Friedman, A.: Modern Analysis. Dover, New York (1982)
Kůrková, V., Neruda, R.: Uniqueness of functional representations by Gaussian basis function networks. In: Proceedings of ICANN 1994, pp. 471–474. Springer, London (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kůrková, V., Kainen, P.C. (2011). Kernel Networks with Fixed and Variable Widths. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20282-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-20282-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20281-0
Online ISBN: 978-3-642-20282-7
eBook Packages: Computer ScienceComputer Science (R0)