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A Bayesian Local Linear Wavelet Neural Network

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Advances in Neuro-Information Processing (ICONIP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5507))

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Abstract

In general, wavelet neural networks have a problem on the curse of dimensionality, i.e. the number of hidden units to be required are exponentially rose with increasing an input dimension. To solve the above problem, a wavelet neural network incorporating a local linear model has already been proposed. On their network design, however, the number of hidden units is empirically determined and fixed during learning. In the present paper, a design method based on Bayesian method is proposed for the local linear wavelet neural network. The performance of the proposed method is evaluated through computer simulation.

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References

  1. Chui, C.K.: An Introduction to Wavelets. Academic Press, London (1992)

    MATH  Google Scholar 

  2. Poggio, T., Girosi, F.: Networks for approximation and learning. Proc. of the IEEE 78(9), 1481–1497 (1990)

    Article  MATH  Google Scholar 

  3. Pati, Y.C., Krishnaprasad, P.S.: Discrete affine wavelet transformations for analysis and synthesis of feedforward neural networks. In: Advances in Neural Information Processing Systems, vol. 3, pp. 743–749. MIT Press, Cambridge (1991)

    Google Scholar 

  4. Zhang, Q., Benveniste, A.: Wavelet networks. IEEE Trans. on Neural Networks 3(6), 889–898 (1992)

    Article  Google Scholar 

  5. Kobayashi, K., Torioka, T., Yoshida, N.: A Wavelet Neural Network with Network Optimizing Function. Systems and Computers in Japan 26(9), 61–71 (1995)

    Article  Google Scholar 

  6. Ueda, N., Kobayashi, K., Torioka, T.: A Wavelet Neural Network with Evolutionally Generated Structures. Trans. on the Institute of Electronics, Information and Communication Engineers J80-D-II(2), 652–659 (1997) (in Japanese)

    Google Scholar 

  7. Wang, T., Sugai, Y.: A local linear adaptive wavelet neural network. Trans. on the Institute of Electrical Engineers of Japan 122-C(2), 277–284 (2002)

    Google Scholar 

  8. Wang, T., Sugai, Y.: The local linear adaptive wavelet neural network with hybrid ep/gradient algorithm and its application to nonlinear dynamic system identification. Trans. on the Institute of Electrical Engineers of Japan 122-C(7), 1194–1201 (2002)

    Google Scholar 

  9. Chen, Y., Dong, J., Yang, B., Zhang, Y.: A local linear wavelet neural network. In: Proc. of the 5th World Congress on Intelligent Control and Automation, pp. 1954–1957 (2004)

    Google Scholar 

  10. Chen, Y., Yang, B., Dong, J.: Time-series prediction using a local linear wavelet neural network. Neurocomputing 69, 449–465 (2006)

    Article  Google Scholar 

  11. MacKay, D.: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  12. Albrecht, S., Busch, J., Kloppenburg, M., Metze, F., Tavan, P.: Generalized radial basis function networks for classification and novelty detection: Self-organization of optimal Bayesian decision. Neural Networks 13, 755–764 (2000)

    Article  Google Scholar 

  13. Andrieu, C., de Freitas, N., Doucet, A.: Robust full Bayesian learning for radial basis networks. Neural Computation 13, 2359–2407 (2001)

    Article  MATH  Google Scholar 

  14. Ueda, N., Nakano, R., Ghahramani, Z., Hinton, G.E.: Split and merge EM algorithm for improving Gaussian mixture density estimates. In: Proc. of the 1998 IEEE Signal Processing Society Workshop, pp. 274–283 (1998)

    Google Scholar 

  15. Sato, M.: Online model selection based on the variational Bayes. Neural Computation 13, 1649–1681 (2001)

    Article  MATH  Google Scholar 

  16. Holmes, C.C., Mallick, B.K.: Bayesian radial basis functions of variable dimension. Neural Computation 10, 1217–1233 (1998)

    Article  Google Scholar 

  17. Sastry, K., Goldberg, D.E.: Probabilistic Model Building and Competent Genetic Programming, pp. 205–220. Kluwer, Dordrecht (2003)

    Google Scholar 

  18. MacKay, D.J.C.: Bayesian interpolation. Neural Computation 4, 415–447 (1992)

    Article  MATH  Google Scholar 

  19. Peterson, C., Anderson, J.R.: A Mean Field Theory Learning Algorithm for Neural Networks. Complex Systems 1, 995–1019 (1987)

    MATH  Google Scholar 

  20. Green, P.J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Attias, H.: Inferring parameter and structure of latent variable models by variational Bayes. In: Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence, pp. 21–30 (1999)

    Google Scholar 

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Kobayashi, K., Obayashi, M., Kuremoto, T. (2009). A Bayesian Local Linear Wavelet Neural Network. In: Köppen, M., Kasabov, N., Coghill, G. (eds) Advances in Neuro-Information Processing. ICONIP 2008. Lecture Notes in Computer Science, vol 5507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03040-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-03040-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03039-0

  • Online ISBN: 978-3-642-03040-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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