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An Adaptively Constructing Multilayer Feedforward Neural Networks Using Hermite Polynomials

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Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence (ICIC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5227))

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Abstract

In this paper a new strategy is introduced for constructing a multi-hidden-layer feedforward neural network (FNN) where each hidden unit employs a polynomial function for its activation function that is different from other units. The proposed scheme incorporates a structure level adaptation as well as a function level adaptation methodologies in constructing the desired network. The activation functions considered consist of orthonormal Hermite polynomials. Using this strategy, a FNN can be constructed as having as many hidden layers and hidden units as dictated by the complexity of the problem being considered.

This research was supported in part by the NSERC (Natural Science and Engineering Research Council of Canada).

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References

  1. Fahlman, S.E.: An Empirical Study of Learning Speed in Back-Propagation Networks. Tech. Rep., CMU-CS-88-162, Carnegie Mellon University (1988)

    Google Scholar 

  2. Fahlman, S.E., Lebiere, C.: The Cascade-correlation Learning Architecture. Tech. Rep., CMU-CS-90-100, Carnegie Mellon University (1991)

    Google Scholar 

  3. Hush, D.R., Horne, B.G.: Progress in Supervised Neural Networks. IEEE Signal Processing Magazine, 8–39 (January 1993)

    Google Scholar 

  4. Hwang, J.N., Lay, S.R., Maechler, M., Martin, R.D., Schimert, J.: Regression Modeling in Back-propagation and Projection Pursuit Learning. IEEE Trans. on Neural Networks 5, 342–353 (1994)

    Article  Google Scholar 

  5. Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers, 2nd edn. McGraw-Hill, New York (1968)

    Google Scholar 

  6. Kwok, T.Y., Yeung, D.Y.: Constructive Algorithms for Structure Learning in Feedforward Neural Networks for Regression Problems. IEEE Trans. on Neural Networks 8(3), 630–645 (1997)

    Article  Google Scholar 

  7. Kwok, T.Y., Yeung, D.Y.: Objective Functions for Training New Hidden Units in Constructive Neural Networks. IEEE Trans. on Neural Networks 8(5), 1131–1148 (1997)

    Article  Google Scholar 

  8. Lau, B., Chao, T.H.: Aided Target Recognition Processing of Mudss Sonar Data. Proceedings of the SPIE 3392, 234–242 (1998)

    Google Scholar 

  9. Linh, T.H., Osowski, S., Stodolski, M.: On-line Heart Beat Recognition Using Hermite Polynomials and Neuro-fuzzy Network. In: IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference, Anchorage, AK, USA, vol. 1, pp. 165–170 (2002)

    Google Scholar 

  10. Pilato, G., Sorbello, F., Vassallo, G.: Using the Hermite Regression Algorithm to Improve the Generalization Capability of a Neural Network. In: Neural Nets WIRN Vietri 1999. Proceedings of the 11th Italian Workshop on Neural Nets, Salerno, Italy, pp. 296–301 (1999)

    Google Scholar 

  11. Rasiah, A.I., Togneri, R., Attikiouzel, Y.: Modeling 1-d Signals Using Hermite Basis Functions. IEE Proc. -Vis. Image Signal Process 144(6), 345–354 (1997)

    Article  Google Scholar 

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De-Shuang Huang Donald C. Wunsch II Daniel S. Levine Kang-Hyun Jo

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© 2008 Springer-Verlag Berlin Heidelberg

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Ma, L., Khorasani, K. (2008). An Adaptively Constructing Multilayer Feedforward Neural Networks Using Hermite Polynomials. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science(), vol 5227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85984-0_77

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  • DOI: https://doi.org/10.1007/978-3-540-85984-0_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85983-3

  • Online ISBN: 978-3-540-85984-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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