Abstract
In this paper we present the method for estimation of unknown function in a time-varying environment. We study the probabilistic neural network based on the Parzen kernels combined with the recursive least square method. We present the conditions for convergence in probability and we discuss the experimental results.
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Albert, A.E., Gardner, L.A.: Stochastic Approximation and Nonlinear Regression, vol. (42). MIT Press, Cambridge (1967)
Benedetti, J.: On the nonparametric estimation of regression function. Journal of Royal Statistical Society B 39, 248–253 (1977)
Bilski, J., Rutkowski, L.: A fast training algorithm for neural networks. IEEE Transactions on Circuits and Systems II 45, 749–753 (1998)
Cacoullos, P.: Estimation of a multivariate density. Annals of the Institute of Statistical Mathematics 18, 179–190 (1965)
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)
Gałkowski, T., Rutkowski, L.: Nonparametric recovery of multivariate functions with applications to system identification. Proceedings of the IEEE 73, 942–943 (1985)
Gałkowski, T., Rutkowski, L.: Nonparametric fitting of multivariable functions. IEEE Transactions on Automatic Control AC-31, 785–787 (1986)
Greblicki, W., Pawlak, M.: Nonparametric system indentification. Cambridge University Press (2008)
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)
Greblicki, W., Rutkowski, L.: Density-free Bayes risk consistency of nonparametric pattern recognition procedures. Proceedings of the IEEE 69(4), 482–483 (1981)
Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-Free Theory of Nonparametric Regression, USA. Springer Series in Statistics (2002)
Härdle, W.: Applied Nonparametric Regression. Cambridge University Press, Cambridge (1990)
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)
Nowicki, R., Pokropińska, A.: Information Criterions Applied to Neuro-Fuzzy Architectures Design. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 332–337. Springer, Heidelberg (2004)
Parzen, E.: On estimation of a probability density function and mode. Analysis of Mathematical Statistics 33(3), 1065–1076 (1962)
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)
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)
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)
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)
Rutkowski, L.: On system identification by nonparametric function fitting. IEEE Transactions on Automatic Control AC-27, 225–227 (1982)
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)
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)
Rutkowski, L.: On-line identification of time-varying systems by nonparametric techniques. IEEE Transactions on Automatic Control AC-27, 228–230 (1982)
Rutkowski, L.: On nonparametric identification with prediction of time-varying systems. IEEE Transactions on Automatic Control AC-29, 58–60 (1984)
Rutkowski, L.: Nonparametric identification of quasi-stationary systems. Systems and Control Letters 6, 33–35 (1985)
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)
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)
Rutkowski, L.: Sequential pattern recognition procedures derived from multiple Fourier series. Pattern Recognition Letters 8, 213–216 (1988)
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)
Rutkowski, L.: An application of multiple Fourier series to identification of multivariable nonstationary systems. International Journal of Systems Science 20(10), 1993–2002 (1989)
Rutkowski, L.: Nonparametric learning algorithms in the time-varying environments. Signal Processing 18, 129–137 (1989)
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)
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)
Rutkowski, L.: Multiple Fourier series procedures for extraction of nonlinear regressions from noisy data. IEEE Transactions on Signal Processing 41(10), 3062–3065 (1993)
Rutkowski, L., Gałkowski, T.: On pattern classification and system identification by probabilistic neural networks. Applied Mathematics and Computer Science 4(3), 413–422 (1994)
Rutkowski, L.: A New Method for System Modelling and Pattern Classification. Bulletin of the Polish Academy of Sciences 52(1), 11–24 (2004)
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)
Rutkowski, L., Cpałka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control and Cybernetics 31(2), 297–308 (2002)
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)
Specht, D.F.: A general regression neural network. IEEE Transactions on Neural Networks 2, 568–576 (1991)
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)
Starczewski, J., 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)
Wilks, S.S.: Mathematical Statistics. John Wiley, New York (1962)
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Hayashi, Y., Pietruczuk, L. (2012). On General Regression Neural Network in a Nonstationary Environment. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_47
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DOI: https://doi.org/10.1007/978-3-642-31464-3_47
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