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Statistical Recognition of a Set of Patterns Using Novel Probability Neural Network

  • Andrey V. Savchenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7477)

Abstract

Since the works by Specht, the probabilistic neural networks (PNNs) have attracted researchers due to their ability to increase training speed and their equivalence to the optimal Bayesian decision of classification task. However, it is known that the PNN’s conventional implementation is not optimal in statistical recognition of a set of patterns. In this article we present the novel modification of the PNN and prove that it is optimal in this task with general assumptions of the Bayes classifier. The modification is based on a reduction of recognition task to homogeneity testing problem. In the experiment we examine a problem of authorship attribution of Russian texts. Our results support the statement that the proposed network provides better accuracy and is much more resistant to change the smoothing parameter of Gaussian kernel function in comparison with the original PNN.

Keywords

Statistical pattern recognition sets of patterns probabilistic neural network hypothesis test for samples homogeneity 

References

  1. 1.
    Theodoridis, S., Koutroumbas, C.: Pattern Recognition, 4th edn. Elsevier Inc. (2009)Google Scholar
  2. 2.
    Borovkov, A.A.: Mathematical Statistics. Gordon and Breach Science Publishers (1998)Google Scholar
  3. 3.
    Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)zbMATHGoogle Scholar
  4. 4.
    Webb, A.R.: Statistical Pattern Recognition. Wiley, New York (2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)zbMATHGoogle Scholar
  6. 6.
    Efromovich, S.: Nonparametric Curve Estimation. Methods, Theory and Applications. Springer, New York (1999)zbMATHGoogle Scholar
  7. 7.
    Murthy, V.K.: Estimation of probability density. Annals of Mathematical Statistics 36, 1027–1031 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Parzen, E.: On estimation of a probability density function and mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Greblicki, W.: Asymptotically optimal pattern recognition procedures with density estimates. IEEE Transactions on Information Theory IT-24, 250–251 (1978)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wolverton, C.T., Wagner, T.J.: Asymptotically optimal discriminant functions for pattern classification. IEEE Transactions on Information Theory 15, 258–265 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Specht, D.F.: Probabilistic neural networks. Neural Networks 3, 109–118 (1990)CrossRefGoogle Scholar
  12. 12.
    Specht, D.F.: Probabilistic Neural Networks for Classification, Mapping, or Associative Memory. In: IEEE International Conference on Neural Networks, vol. I, pp. 525–532 (1988)Google Scholar
  13. 13.
    Specht, D.F.: A general regression neural network. IEEE Transactions on Neural Networks 2(6), 568–576 (1991)CrossRefGoogle Scholar
  14. 14.
    Rutkowski, L.: Adaptive Probabilistic Neural Networks for Pattern Classification in Time-Varying Environment. IEEE Transactions on Neural Networks 15(4), 811–827 (2004)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kullback, S.: Information Theory and Statistics. Dover Pub. (1997)Google Scholar
  16. 16.
    Jones, M.C., Marron, J.S., Sheather, S.J.: A brief survey of bandwidh selection for density estimation. Journal of the American Statistical Association 91, 401–407 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Kukushkina, O.V., Polikarpov, A.A., Khmelev, D.V.: Using Literal and Grammatical Statistics for Authorship Attribution. Problems of Information Transmission 37(2), 172–184 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    The e-library of Maxim Moshkov, http://www.lib.ru
  19. 19.
    Savchenko, A.V.: Image Recognition with a Large Database Using Method of Directed Enumeration Alternatives Modification. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds.) RSFDGrC 2011. LNCS (LNAI), vol. 6743, pp. 338–341. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Savchenko, A.V.: Directed enumeration method in image recognition. Pattern Recognition 45(8), 2952–2961 (2012)CrossRefGoogle Scholar
  21. 21.
    Aizerman, M.A., Braverman, E.M., Rozonoer, L.I.: Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control 25, 821–837 (1964)MathSciNetGoogle Scholar
  22. 22.
    Stamatatos, E.: A survey of modern authorship attribution methods. Journal of the American Society for Information Science and Technology 60(3), 538–556 (2009)CrossRefGoogle Scholar
  23. 23.
    Mao, K.Z., Tan, K.-C., Ser, W.: Probabilistic neural-network structure determination for pattern classification. IEEE Transactions on Neural Networks 11, 1009–1016 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrey V. Savchenko
    • 1
  1. 1.National Research University Higher School of EconomicsNizhniy NovgorodRussian Federation

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