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2018 | OriginalPaper | Buchkapitel

5. Radial Basis Function Networks

verfasst von : Charu C. Aggarwal

Erschienen in: Neural Networks and Deep Learning

Verlag: Springer International Publishing

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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.

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Fußnoten
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].
 
Literatur
[6]
Zurück zum Zitat C. Aggarwal. Machine learning for text. Springer, 2018. C. Aggarwal. Machine learning for text. Springer, 2018.
[41]
Zurück zum Zitat C. M. Bishop. Neural networks for pattern recognition. Oxford University Press, 1995. C. M. Bishop. Neural networks for pattern recognition. Oxford University Press, 1995.
[43]
Zurück zum Zitat C. M Bishop. Improving the generalization properties of radial basis function neural networks. Neural Computation, 3(4), pp. 579–588, 1991. C. M Bishop. Improving the generalization properties of radial basis function neural networks. Neural Computation, 3(4), pp. 579–588, 1991.
[51]
Zurück zum Zitat D. Broomhead and D. Lowe. Multivariable functional interpolation and adaptive networks. Complex Systems, 2, pp. 321–355, 1988.MathSciNetMATH D. Broomhead and D. Lowe. Multivariable functional interpolation and adaptive networks. Complex Systems, 2, pp. 321–355, 1988.MathSciNetMATH
[57]
Zurück zum Zitat M. Buhmann. Radial Basis Functions: Theory and implementations. Cambridge University Press, 2003. M. Buhmann. Radial Basis Functions: Theory and implementations. Cambridge University Press, 2003.
[65]
Zurück zum Zitat 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 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
[84]
Zurück zum Zitat 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. 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.
[125]
Zurück zum Zitat B. Fritzke. Fast learning with incremental RBF networks. Neural Processing Letters, 1(1), pp. 2–5, 1994.CrossRef B. Fritzke. Fast learning with incremental RBF networks. Neural Processing Letters, 1(1), pp. 2–5, 1994.CrossRef
[173]
Zurück zum Zitat 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 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
[182]
Zurück zum Zitat S. Haykin. Neural networks and learning machines. Pearson, 2008. S. Haykin. Neural networks and learning machines. Pearson, 2008.
[256]
Zurück zum Zitat M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5), pp. 813–821, 1998.MathSciNetCrossRef M. Kubat. Decision trees can initialize radial-basis function networks. IEEE Transactions on Neural Networks, 9(5), pp. 813–821, 1998.MathSciNetCrossRef
[323]
Zurück zum Zitat C. Micchelli. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constructive Approximations, 2, pp. 11–22, 1986.MathSciNetCrossRef C. Micchelli. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constructive Approximations, 2, pp. 11–22, 1986.MathSciNetCrossRef
[342]
Zurück zum Zitat J. Moody and C. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1(2), pp. 281–294, 1989.CrossRef J. Moody and C. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1(2), pp. 281–294, 1989.CrossRef
[347]
Zurück zum Zitat 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 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
[365]
Zurück zum Zitat J. Park and I. Sandberg. Universal approximation using radial-basis-function networks. Neural Computation, 3(1), pp. 246–257, 1991.CrossRef J. Park and I. Sandberg. Universal approximation using radial-basis-function networks. Neural Computation, 3(1), pp. 246–257, 1991.CrossRef
[366]
Zurück zum Zitat J. Park and I. Sandberg. Approximation and radial-basis-function networks. Neural Computation, 5(2), pp. 305–316, 1993.CrossRef J. Park and I. Sandberg. Approximation and radial-basis-function networks. Neural Computation, 5(2), pp. 305–316, 1993.CrossRef
[423]
Zurück zum Zitat 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 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
[430]
Zurück zum Zitat 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 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
[530]
Zurück zum Zitat D. Wettschereck and T. Dietterich. Improving the performance of radial basis function networks by learning center locations. NIPS Conference, pp. 1133–1140, 1992. D. Wettschereck and T. Dietterich. Improving the performance of radial basis function networks by learning center locations. NIPS Conference, pp. 1133–1140, 1992.
Metadaten
Titel
Radial Basis Function Networks
verfasst von
Charu C. Aggarwal
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-94463-0_5

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