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.
Chapter PDF
Similar content being viewed by others
Keywords
References
Theodoridis, S., Koutroumbas, C.: Pattern Recognition, 4th edn. Elsevier Inc. (2009)
Borovkov, A.A.: Mathematical Statistics. Gordon and Breach Science Publishers (1998)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
Webb, A.R.: Statistical Pattern Recognition. Wiley, New York (2002)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)
Efromovich, S.: Nonparametric Curve Estimation. Methods, Theory and Applications. Springer, New York (1999)
Murthy, V.K.: Estimation of probability density. Annals of Mathematical Statistics 36, 1027–1031 (1965)
Parzen, E.: On estimation of a probability density function and mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)
Greblicki, W.: Asymptotically optimal pattern recognition procedures with density estimates. IEEE Transactions on Information Theory IT-24, 250–251 (1978)
Wolverton, C.T., Wagner, T.J.: Asymptotically optimal discriminant functions for pattern classification. IEEE Transactions on Information Theory 15, 258–265 (1969)
Specht, D.F.: Probabilistic neural networks. Neural Networks 3, 109–118 (1990)
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)
Specht, D.F.: A general regression neural network. IEEE Transactions on Neural Networks 2(6), 568–576 (1991)
Rutkowski, L.: Adaptive Probabilistic Neural Networks for Pattern Classification in Time-Varying Environment. IEEE Transactions on Neural Networks 15(4), 811–827 (2004)
Kullback, S.: Information Theory and Statistics. Dover Pub. (1997)
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)
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)
The e-library of Maxim Moshkov, http://www.lib.ru
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)
Savchenko, A.V.: Directed enumeration method in image recognition. Pattern Recognition 45(8), 2952–2961 (2012)
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)
Stamatatos, E.: A survey of modern authorship attribution methods. Journal of the American Society for Information Science and Technology 60(3), 538–556 (2009)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Savchenko, A.V. (2012). Statistical Recognition of a Set of Patterns Using Novel Probability Neural Network. In: Mana, N., Schwenker, F., Trentin, E. (eds) Artificial Neural Networks in Pattern Recognition. ANNPR 2012. Lecture Notes in Computer Science(), vol 7477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33212-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-33212-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33211-1
Online ISBN: 978-3-642-33212-8
eBook Packages: Computer ScienceComputer Science (R0)