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Radial Basis Function Networks

Abstract

Radial basis function (RBF) networks represent a fundamentally different architecture from what we have seen in the previous chapters. All the previous chapters use a feed-forward network in which the inputs are transmitted forward from layer to layer in a similar fashion in order to create the final outputs.

Keywords

  • Prototype Vectors
  • Orthogonal Least Squares Algorithm
  • Perceptron Criterion
  • Training Points
  • Kernel Regression

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

“Two birds disputed about a kernel, when a third swooped down and carried it off.”—African Proverb

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Figure 5.1
Figure 5.2

Notes

  1. 1.

    A full explanation of the kernel regression prediction of Equation 5.18 is beyond the scope of this book. Readers are referred to [6].

Bibliography

  1. C. Aggarwal. Machine learning for text. Springer, 2018.

    Google Scholar 

  2. C. M. Bishop. Neural networks for pattern recognition. Oxford University Press, 1995.

    Google Scholar 

  3. C. M Bishop. Improving the generalization properties of radial basis function neural networks. Neural Computation, 3(4), pp. 579–588, 1991.

    Google Scholar 

  4. D. Broomhead and D. Lowe. Multivariable functional interpolation and adaptive networks. Complex Systems, 2, pp. 321–355, 1988.

    MathSciNet  MATH  Google Scholar 

  5. M. Buhmann. Radial Basis Functions: Theory and implementations. Cambridge University Press, 2003.

    Google Scholar 

  6. S. Chen, C. Cowan, and P. Grant. Orthogonal least-squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks, 2(2), pp. 302–309, 1991.

    CrossRef  Google Scholar 

  7. T. Cover. Geometrical and statistical properties of systems of linear inequalities with applications to pattern recognition. IEEE Transactions on Electronic Computers, pp. 326–334, 1965.

    Google Scholar 

  8. B. Fritzke. Fast learning with incremental RBF networks. Neural Processing Letters, 1(1), pp. 2–5, 1994.

    CrossRef  Google Scholar 

  9. E. Hartman, J. Keeler, and J. Kowalski. Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation, 2(2), pp. 210–215, 1990.

    CrossRef  Google Scholar 

  10. S. Haykin. Neural networks and learning machines. Pearson, 2008.

    Google Scholar 

  11. M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5), pp. 813–821, 1998.

    MathSciNet  CrossRef  Google Scholar 

  12. C. Micchelli. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constructive Approximations, 2, pp. 11–22, 1986.

    MathSciNet  CrossRef  Google Scholar 

  13. J. Moody and C. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1(2), pp. 281–294, 1989.

    CrossRef  Google Scholar 

  14. M. Musavi, W. Ahmed, K. Chan, K. Faris, and D. Hummels. On the training of radial basis function classifiers. Neural Networks, 5(4), pp. 595–603, 1992.

    CrossRef  Google Scholar 

  15. M. J. L. Orr. Introduction to radial basis function networks, University of Edinburgh Technical Report, Centre of Cognitive Science, 1996. ftp://ftp.cogsci.ed.ac.uk/pub/mjo/intro.ps.Z

  16. J. Park and I. Sandberg. Universal approximation using radial-basis-function networks. Neural Computation, 3(1), pp. 246–257, 1991.

    CrossRef  Google Scholar 

  17. J. Park and I. Sandberg. Approximation and radial-basis-function networks. Neural Computation, 5(2), pp. 305–316, 1993.

    CrossRef  Google Scholar 

  18. H. Sarimveis, A. Alexandridis, and G. Bafas. A fast training algorithm for RBF networks based on subtractive clustering. Neurocomputing, 51, pp. 501–505, 2003.

    CrossRef  Google Scholar 

  19. B. Schölkopf, K. Sung, C. Burges, F. Girosi, P. Niyogi, T. Poggio, and V. Vapnik. Comparing support vector machines with Gaussian kernels to radial basis function classifiers. IEEE Transactions on Signal Processing, 45(11), pp. 2758–2765, 1997.

    CrossRef  Google Scholar 

  20. D. Wettschereck and T. Dietterich. Improving the performance of radial basis function networks by learning center locations. NIPS Conference, pp. 1133–1140, 1992.

    Google Scholar 

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Aggarwal, C.C. (2018). Radial Basis Function Networks. In: Neural Networks and Deep Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-94463-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-94463-0_5

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