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Optimization of Centers’ Positions for RBF Nets with Generalized Kernels

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Book cover Artificial Intelligence and Soft Computing - ICAISC 2004 (ICAISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3070))

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Abstract

The problem of locating centers for radial basis functions in neural networks is discussed. The proposed approach allows us to apply the results from the theory of optimum experimental designs. In typical cases we are able to compose optimal centers’ locations from the known univariate experiment designs.

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References

  1. Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)

    Google Scholar 

  2. Karlin, S., Studden, W.J.: Tchebycheff Systems, with Applications in Analysis and Statistics. Interscience, New York (1972)

    Google Scholar 

  3. Lankaster, P.: Theory of Matrices. Academic Press, London (1969)

    Google Scholar 

  4. Mao, K.Z.R.: neural network center selection based on Fisher ratio class separability measure. IEEE Transactions on Neural Networks 13, 1211–1217 (2002)

    Article  Google Scholar 

  5. Mitchell, T.J.: An algorithm for the construction of ”D-optimal” experimental designs. Technometrics 16, 203–210 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Panchapakesan, C., Palaniswami, M., Ralph, D., Manzie, C.: Effects of moving the centers in an RBF network. IEEE Transactions on Neural Networks 13, 1299–1307 (2002)

    Article  Google Scholar 

  7. Park, J., Sandberg, I.: Universal approximation using radial basis function networks. Neural Computation 3, 246–257 (1991)

    Article  Google Scholar 

  8. Rafajlowicz, E., Myszka, W.: Optimum experimental design for a regression on a hypercube – generalization of Hoel’s result. Ann. Inst. Statist. Math. 40, 821–827 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Schoenberg, I.J.: Metric spaces and completely monotone functions. Ann. of Math. 39, 811–841 (1938)

    Article  MathSciNet  Google Scholar 

  10. Tricomi, F.G.: Integral Equations. Dover, New York (1985)

    Google Scholar 

  11. Xu, L., Krzyzak, A., Yuille, A.: On radial basis function nets and kernel regression: Statistical consistency, convergence rates, and receptive field size. Neural Networks 4, 609–628 (1994)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Engineering Cybernetis, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50 370, Wrocław, Poland

    E. Rafajłowicz

  2. Department of Electrical and Computer Engineering University of Manitoba, Winnipeg, Canada

    M. Pawlak

Authors
  1. E. Rafajłowicz
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  2. M. Pawlak
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Editor information

Editors and Affiliations

  1. Department of Artificial Intelligence, Academy of Humanities and Economics, Poland

    Leszek Rutkowski

  2. German Research Center of Artificial Intelligence (DFKI), Germany

    Jörg H. Siekmann

  3. Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, PL-30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Initiative in Soft Computing (BISC), 94720-1776, Berkeley, CA

    Lotfi A. Zadeh

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© 2004 Springer-Verlag Berlin Heidelberg

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Rafajłowicz, E., Pawlak, M. (2004). Optimization of Centers’ Positions for RBF Nets with Generalized Kernels. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds) Artificial Intelligence and Soft Computing - ICAISC 2004. ICAISC 2004. Lecture Notes in Computer Science(), vol 3070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24844-6_34

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  • DOI: https://doi.org/10.1007/978-3-540-24844-6_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22123-4

  • Online ISBN: 978-3-540-24844-6

  • eBook Packages: Springer Book Archive

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