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Multilayer Perceptron Learning Utilizing Reducibility Mapping

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Computational Intelligence (IJCCI 2011)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 465))

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Abstract

In the search space of MLP(J), multilayer perceptron having J hidden units, there exist flat areas called singular regions created by applying reducibility mapping to the optimal solution of MLP(Jā€‰āˆ’1). Since such singular regions cause serious slowdown for learning, a learning method for avoiding singular regions has been aspired. However, such avoiding does not guarantee the quality of the final solutions. This paper proposes a new learning method which does not avoid but makes good use of singular regions to stably and successively find solutions excellent enough for MLP(J). The potential of the method is shown by our experiments using artificial and real data sets.

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References

  1. Amari, S.: Natural gradient works efficiently in learning. Neural ComputationĀ 10(2), 251ā€“276 (1998)

    ArticleĀ  Google ScholarĀ 

  2. Amari, S., Park, H., Fukumizu, K.: Adaptive method of realizing natural gradient learning for multilayer perceptrons. Neural ComputationĀ 12(6), 1399ā€“1409 (2000)

    ArticleĀ  Google ScholarĀ 

  3. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern classification, 2nd edn. John Wiley & Sons, Inc. (2001)

    Google ScholarĀ 

  4. Fukumizu, K., Amari, S.: Local minima and plateaus in hierarchical structure of multilayer perceptrons. Neural NetworksĀ 1(3), 317ā€“327 (2000)

    ArticleĀ  Google ScholarĀ 

  5. Hamey, L.G.C.: XOR has no local minima: a case study in neural network error surface. Neural NetworksĀ 11(4), 669ā€“681 (1998)

    ArticleĀ  Google ScholarĀ 

  6. Minnett, R.C.J., Smith, A.T., Lennon Jr., W.C., Hecht-Nielsen, R.: Neural network tomography: network replication from output surface geometry. Neural NetworksĀ 24(5), 484ā€“492 (2011)

    ArticleĀ  Google ScholarĀ 

  7. Luenberger, D.G.: Linear and nonlinear programming. Addison-Wesley (1984)

    Google ScholarĀ 

  8. Nakano, R., Saito, K.: Discovering Polynomials to Fit Multivariate Data Having Numeric and Nominal Variables. In: Arikawa, S., Shinohara, A. (eds.) Progress in Discovery Science. LNCS (LNAI), vol.Ā 2281, pp. 482ā€“493. Springer, Heidelberg (2002)

    ChapterĀ  Google ScholarĀ 

  9. Nakano, R., Satoh, S., Ohwaki, T.: Learning method utilizing singular region of multilayer perceptron. In: Proc. 3rd Int. Conf. on Neural Computation Theory and Applications, pp. 106ā€“111 (2011)

    Google ScholarĀ 

  10. Watanabe, S.: Algebraic geometry and statistical learning theory. Cambridge Univ. Press (2009)

    Google ScholarĀ 

  11. Saito, K., Nakano, R.: Partial BFGS update and efficient step-length calculation for three-layer neural networks. Neural ComputationĀ 9(1), 239ā€“257 (1997)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  12. Sussmann, H.J.: Uniqueness of the weights for minimal feedforward nets with a given input-output map. Neural NetworksĀ 5(4), 589ā€“593 (1992)

    ArticleĀ  Google ScholarĀ 

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Correspondence to Seiya Satoh .

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Satoh, S., Nakano, R. (2013). Multilayer Perceptron Learning Utilizing Reducibility Mapping. In: Madani, K., Dourado, A., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2011. Studies in Computational Intelligence, vol 465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35638-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-35638-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35637-7

  • Online ISBN: 978-3-642-35638-4

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