Skip to main content
SpringerLink
Log in
Book cover

International Conference on Artificial Intelligence and Soft Computing

ICAISC 2012: Artificial Intelligence and Soft Computing pp 99–110Cite as

On Learning in a Time-Varying Environment by Using a Probabilistic Neural Network and the Recursive Least Squares Method

  • Conference paper

  • 2199 Accesses

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

Abstract

This paper presents the recursive least squares method, combined with the general regression neural networks, applied to solve the problem of learning in time-varying environment. The general regression neural network is based on the orthogonal-type kernel functions. The appropriate algorithm is presented in a recursive form. Sufficient simulations confirm empirically the convergence of the algorithm.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, A.E., Gardner, L.A.: Stochastic Approximation and Nonlinear Regression, No. 42. MIT Press, Cambridge (1967)

    MATH  Google Scholar 

  2. 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 

  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. 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 

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

    Article  MATH  Google Scholar 

  6. Greblicki, W., Pawlak, M.: Nonparametric system indentification. Cambridge University Press (2008)

    Google Scholar 

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

    Google Scholar 

  8. 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 

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

    Book  MATH  Google Scholar 

  10. Nowicki, R.: Nonlinear modelling and classification based on the MICOG defuzzifications. Journal of Nonlinear Analysis, Series A: Theory, Methods and Applications 7(12), 1033–1047 (2009)

    Article  Google Scholar 

  11. 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 

  12. 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 

  13. 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)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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 

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

    Article  MATH  Google Scholar 

  16. 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 

  17. 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  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. 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 

  22. 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  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  24. 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 

  25. 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 

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

    Article  MathSciNet  Google Scholar 

  27. 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  MATH  Google Scholar 

  28. 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  MATH  Google Scholar 

  29. 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 

  30. 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 

  31. 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 

  32. 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 

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

    MATH  Google Scholar 

  34. 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 

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

    Article  Google Scholar 

  36. Specht, D.F.: A general regression neural network. IEEE Transactions on Neural Networks 2, 568–576 (1991)

    Article  Google Scholar 

  37. Starczewski, J., 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 

  38. 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 

  39. Szegö, G.: Orthogonal Polynomials, vol. 23. American Mathematical Society Coll. Publ. (1959)

    Google Scholar 

  40. Wilks, S.S.: Mathematical Statistics. John Wiley, New York (1962)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Maciej Jaworski & Marcin Gabryel

Authors
  1. Maciej Jaworski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcin Gabryel
    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

Jaworski, M., Gabryel, M. (2012). On Learning in a Time-Varying Environment by Using a Probabilistic Neural Network and the Recursive Least Squares Method. 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_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29347-4_12

  • 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