Skip to main content
SpringerLink
Log in

Weak Convergence of the Parzen-Type Probabilistic Neural Network Handling Time-Varying Noise

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

Included in the following conference series:

  • 2191 Accesses

Abstract

In this paper we study probabilistic neural networks based on the Parzen kernels. Weak convergence is established assuming time-varying noise. Simulation results are discussed in details.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bilski, J., Rutkowski, L.: A fast training algorithm for neural networks. IEEE Transactions on Circuits and Systems II 45, 749–753 (1998)

    Article  Google Scholar 

  2. Cacoullos, P.: Estimation of a multivariate density. Annals of the Institute of Statistical Mathematics 18, 179–190 (1965)

    Article  MathSciNet  Google Scholar 

  3. Cierniak, R., Rutkowski, L.: On image compression by competitive neural networks and optimal linear predictors. Signal Processing: Image Communication - a Eurasip Journal 15(6), 559–565 (2000)

    Article  Google Scholar 

  4. Chu, C.K., Marron, J.S.: Choosing a kernel regression estimator. Statistical Science 6, 404–436 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gałkowski, T., Rutkowski, L.: Nonparametric recovery of multivariate functions with applications to system identification. Proceedings of the IEEE 73, 942–943 (1985)

    Article  Google Scholar 

  6. Gałkowski, T., Rutkowski, L.: Nonparametric fitting of multivariable functions. IEEE Transactions on Automatic Control AC-31, 785–787 (1986)

    Article  Google Scholar 

  7. Greblicki, W., Pawlak, M.: Nonparametric system identification. Cambridge University Press (2008)

    Google Scholar 

  8. Greblicki, W., Rutkowska, D., Rutkowski, L.: An orthogonal series estimate of time-varying regression. Annals of the Institute of Statistical Mathematics 35, Part A, 147–160 (1983)

    MathSciNet  Google Scholar 

  9. Greblicki, W., Rutkowski, L.: Density-free Bayes risk consistency of nonparametric pattern recognition procedures. Proceedings of the IEEE 69(4), 482–483 (1981)

    Article  Google Scholar 

  10. Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-Free Theory of Nonparametric Regression. Springer Series in Statistics, USA (2002)

    Book  MATH  Google Scholar 

  11. Härdle, W.: Applied Nonparametric Regression. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  12. Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-Free Theory of Nonparameric Regression. Springer Series in Statistics, USA (2002)

    Book  Google Scholar 

  13. Nowicki, R.: Rough Sets in the Neuro-Fuzzy Architectures Based on Non-monotonic Fuzzy Implications. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 518–525. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Ozden, M., Polat, E.: A color image segmentation approach for content-based image retrieval. Pattern Recognition 40, 1318–1325 (2007)

    Article  MATH  Google Scholar 

  15. Parzen, E.: On estimation of a probability density function and mode. Analysis of Mathematical Statistics 33(3), 1065–1076 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  16. Patan, K., Patan, M.: Optimal training strategies for locally recurrent neural networks. Journal of Artificial Intelligence and Soft Computing Research 1(2), 103–114 (2011)

    Google Scholar 

  17. Rafajłowicz, E.: Nonparametric orthogonal series estimators of regression: A class attaining the optimal convergence rate in L 2. Statistics and Probability Letters 5, 219–224 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rutkowski, L.: Sequential estimates of probability densities by orthogonal series and their application in pattern classification. IEEE Transactions on Systems, Man, and Cybernetics SMC-10(12), 918–920 (1980)

    MathSciNet  Google Scholar 

  19. Rutkowski, L.: Sequential estimates of a regression function by orthogonal series with applications in discrimination, New York-Heidelberg-Berlin. Lectures Notes in Statistics, vol. 8, pp. 236–244 (1981)

    Google Scholar 

  20. Rutkowski, L.: On system identification by nonparametric function fitting. IEEE Transactions on Automatic Control AC-27, 225–227 (1982)

    Article  Google Scholar 

  21. Rutkowski, L.: Orthogonal series estimates of a regression function with applications in system identification. In: Probability and Statistical Inference, pp. 343–347. D. Reidel Publishing Company, Dordrecht (1982)

    Chapter  Google Scholar 

  22. Rutkowski, L.: On Bayes risk consistent pattern recognition procedures in a quasi-stationary environment. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-4(1), 84–87 (1982)

    Article  MathSciNet  Google Scholar 

  23. Rutkowski, L.: On-line identification of time-varying systems by nonparametric techniques. IEEE Transactions on Automatic Control AC-27, 228–230 (1982)

    Article  Google Scholar 

  24. Rutkowski, L.: On nonparametric identification with prediction of time-varying systems. IEEE Transactions on Automatic Control AC-29, 58–60 (1984)

    Article  Google Scholar 

  25. Rutkowski, L.: Nonparametric identification of quasi-stationary systems. Systems and Control Letters 6, 33–35 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  26. Rutkowski, L.: The real-time identification of time-varying systems by nonparametric algorithms based on the Parzen kernels. International Journal of Systems Science 16, 1123–1130 (1985)

    Article  MATH  Google Scholar 

  27. Rutkowski, L.: A general approach for nonparametric fitting of functions and their derivatives with applications to linear circuits identification. IEEE Transactions Circuits Systems CAS-33, 812–818 (1986)

    Article  Google Scholar 

  28. Rutkowski, L.: Sequential pattern recognition procedures derived from multiple Fourier series. Pattern Recognition Letters 8, 213–216 (1988)

    Article  MATH  Google Scholar 

  29. Rutkowski, L.: Nonparametric procedures for identification and control of linear dynamic systems. In: Proceedings of 1988 American Control Conference, June 15-17, pp. 1325–1326 (1988)

    Google Scholar 

  30. Rutkowski, L.: An application of multiple Fourier series to identification of multivariable nonstationary systems. International Journal of Systems Science 20(10), 1993–2002 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  31. Rutkowski, L.: Nonparametric learning algorithms in the time-varying environments. Signal Processing 18, 129–137 (1989)

    Article  MathSciNet  Google Scholar 

  32. Rutkowski, L., Rafajłowicz, E.: On global rate of convergence of some nonparametric identification procedures. IEEE Transaction on Automatic Control AC-34(10), 1089–1091 (1989)

    Article  Google Scholar 

  33. Rutkowski, L.: Identification of MISO nonlinear regressions in the presence of a wide class of disturbances. IEEE Transactions on Information Theory IT-37, 214–216 (1991)

    Article  MathSciNet  Google Scholar 

  34. Rutkowski, L.: Multiple Fourier series procedures for extraction of nonlinear regressions from noisy data. IEEE Transactions on Signal Processing 41(10), 3062–3065 (1993)

    Article  MATH  Google Scholar 

  35. Rutkowski, L., Gałkowski, T.: On pattern classification and system identification by probabilistic neural networks. Applied Mathematics and Computer Science 4(3), 413–422 (1994)

    Google Scholar 

  36. Rutkowski, L.: A New Method for System Modelling and Pattern Classification. Bulletin of the Polish Academy of Sciences 52(1), 11–24 (2004)

    MathSciNet  MATH  Google Scholar 

  37. Rutkowski, L., Cpałka, K.: A general approach to neuro - fuzzy systems. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, Melbourne, December 2-5, vol. 3, pp. 1428–1431 (2001)

    Google Scholar 

  38. Rutkowski, L., Cpałka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control and Cybernetics 31(2), 297–308 (2002)

    MATH  Google Scholar 

  39. Scherer, R.: Boosting Ensemble of Relational Neuro-fuzzy Systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 306–313. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  40. Specht, D.F.: Probabilistic neural networks. Neural Networks 3, 109–118 (1990)

    Article  Google Scholar 

  41. Starczewski, L., Rutkowski, L.: Interval type 2 neuro-fuzzy systems based on interval consequents. In: Rutkowski, L., Kacprzyk, J. (eds.) Neural Networks and Soft Computing, pp. 570–577. Physica-Verlag, Springer-Verlag Company, Heidelberg, New York (2003)

    Google Scholar 

  42. Starczewski, J.T., Rutkowski, L.: Connectionist Structures of Type 2 Fuzzy Inference Systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 634–642. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Czestochowa University of Technology, ul. Armii Krajowej 36, 42-200, Czestochowa, Poland

    Lena Pietruczuk

  2. School of Electrical & Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798

    Meng Joo Er

Authors
  1. Lena Pietruczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng Joo Er
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, Computer Science Division, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pietruczuk, L., Er, M.J. (2012). Weak Convergence of the Parzen-Type Probabilistic Neural Network Handling Time-Varying Noise. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29347-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation