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Simultaneous Learning of Several Bayesian and Mahalanobis Discriminant Functions by a Neural Network with Memory Nodes

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7667)

Abstract

We construct a one-hidden-layer neural network capable of learning simultaneously several Bayesian discriminant functions and converting them to the corresponding Mahalanobis discriminant functions in the two-category, normal-distribution case. The Bayesian discriminant functions correspond to the respective situations on which the priors and means depend. The algorithm is characterized by the use of the inner potential of the output unit and additional several memory nodes. It is remarkably simpler when compared with our previous algorithm.

Keywords

  • Simultaneous learning
  • Discriminant function
  • Bayesian
  • Mahalanobis

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References

  1. Funahashi, K.: Multilayer Neural Networks and Bayes Decision Theory. Neural Networks 11, 209–213 (1998)

    CrossRef  Google Scholar 

  2. Ito, Y., Srinivasan, C.: Multicategory Bayesian Decision Using a Three-layer Neural Network. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 253–261. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  3. Ito, Y., Srinivasan, C.: Bayesian Decision Theory on Three-layer neural networks. Neurocomput. 63, 209–228 (2005)

    CrossRef  Google Scholar 

  4. Ito, Y., Srinivasan, C., Izumi, H.: Bayesian Learning of Neural Networks Adapted to Changes of Prior Probabilities. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 253–259. Springer, Heidelberg (2005)

    Google Scholar 

  5. Ito, Y., Srinivasan, C., Izumi, H.: Discriminant Analysis by a Neural Network with Mahalanobis Distance. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4132, pp. 350–360. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  6. Ito, Y.: Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks. Neural Comput. 20, 2757–2791 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Ito, Y., Srinivasan, C., Izumi, H.: Learning of Bayesian Discriminant Functions by a Layered Neural Network. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds.) ICONIP 2007, Part I. LNCS, vol. 4984, pp. 238–247. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  8. Ito, Y., Srinivasan, C., Izumi, H.: Multi-category Bayesian Decision by Neural Networks. In: Kůrková, V., Neruda, R., Koutník, J. (eds.) ICANN 2008, Part I. LNCS, vol. 5163, pp. 21–30. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  9. Ito, Y., Izumi, H., Srinivasan, C.: Learning of Mahalanobis Discriminant Functions by a Neural Network. In: Leung, C.S., Lee, M., Chan, J.H. (eds.) ICONIP 2009, Part I. LNCS, vol. 5863, pp. 417–424. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  10. Ito, Y., Izumi, H., Srinivasan, C.: Simultaneous Learning of Several Bayesian and Mahalanobis Discriminant Functions by a Neural Network with Additional Nodes. Australian J. Intell. Inform. Process. Syst. 11, 1–7 (2010); Proceedings of ICONIP 2010

    Google Scholar 

  11. Ito, Y., Izumi, H., Srinivasan, C.: Learning of Mahalanobis Discriminant Functions by a Neural Network (submitted, preparation)

    Google Scholar 

  12. Richard, M.D., Lipmann, R.P.: Neural Network Classifiers Estimate Bayesian a Posteriori Probabilities. Neural Comput. 3, 461–483 (1991)

    CrossRef  Google Scholar 

  13. Ruck, M.D., Rogers, S., Kabrisky, M., Oxley, H., Sutter, B.: The Multilayer Perceptron as Approximator to a Bayes Optimal Discriminant Function. IEEE Trans. Neural Networks 1, 296–298 (1990)

    CrossRef  Google Scholar 

  14. White, H.: Learning in Artificial Neural Networks: A Statistical Perspective. Neural Comput. 1, 425–464 (1989)

    CrossRef  Google Scholar 

  15. Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Joh Wiley & Sons, New York (1973)

    MATH  Google Scholar 

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Ito, Y., Izumi, H., Srinivasan, C. (2012). Simultaneous Learning of Several Bayesian and Mahalanobis Discriminant Functions by a Neural Network with Memory Nodes. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34500-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-34500-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34499-2

  • Online ISBN: 978-3-642-34500-5

  • eBook Packages: Computer ScienceComputer Science (R0)