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.
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References
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)
Chu, C.K., Marron, J.S.: Choosing a kernel regression estimator. Statistical Science 6, 404–436 (1991)
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 identification. 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. Springer Series in Statistics, USA (2002)
Härdle, W.: Applied Nonparametric Regression. Cambridge University Press, Cambridge (1990)
Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-Free Theory of Nonparameric Regression. Springer Series in Statistics, USA (2002)
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)
Ozden, M., Polat, E.: A color image segmentation approach for content-based image retrieval. Pattern Recognition 40, 1318–1325 (2007)
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.: Probabilistic neural networks. Neural Networks 3, 109–118 (1990)
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.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)
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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
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DOI: https://doi.org/10.1007/978-3-642-29347-4_18
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