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Admissibility and optimality of the cascade-correlation algorithm

  • Part III: Learning: Theory and Algorithms
  • Conference paper
  • First Online:
Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

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Abstract

This contribution considers some convergence and optimality properties of the Cascade-Correlation Algorithm (CCA). It is proved, that arbitrary, non-contradicting learning tasks can be solved with linear output neurons within a finite number of steps. Furthermore, it is shown that the correlation criterion proposed by Fahlman [3] does not necessarily choose optimal weights. An optimal criterion is given for linear output neurons. For nonlinear output neurons it is demonstrated, that the CCA does not need to converge even for finite learning tasks. Thus, it is generally not an universal approximation tool.

This work was supported by the Thuringian Ministry for Science, Research and Arts (project ITHERA, B511-95004).

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References

  1. A. Doering. Optimization of Feature Extraction and Classifier Structure for Pattern Recognition with Neural Networks. PhD thesis, TU Dresden, 1997.

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  2. G.P. Drago and S. Ridella. Convergence properties of cascade correlation in function approximation. Neural Comput. and Applic., 2:142–7, 1994.

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  3. S. E. Fahlman and C. Lebiere. The cascade-correlation learning architecture. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems, volume 2, pages 524–532, Denver 1989, 1990. Morgan Kaufmann, San Mateo.

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  4. J.N. Hwang, S.S. You, S.R. Lay, and I.C. Jou. The cascade-correlation learning: A projection pursuit learning perspective. IEEE Transactions on Neural Networks, 7(2):278–89, March 1996.

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Authors and Affiliations

  1. Institute for Medical Statistics, Computer Sciences and Documentation, Friedrich Schiller University Jena, Germany

    A. Doering, M. Galicki & H. Witte

Authors
  1. A. Doering
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  2. M. Galicki
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  3. H. Witte
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Editor information

Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

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© 1997 Springer-Verlag Berlin Heidelberg

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Doering, A., Galicki, M., Witte, H. (1997). Admissibility and optimality of the cascade-correlation algorithm. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020205

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  • DOI: https://doi.org/10.1007/BFb0020205

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

  • eBook Packages: Springer Book Archive

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