On General Regression Neural Network in a Nonstationary Environment

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.

[1]  Leszek Rutkowski,et al.  A general approach for nonparametric fitting of functions and their derivatives with applications to linear circuits identification , 1986 .

[2]  L. Rutkowski,et al.  Nonparametric fitting of multivariate functions , 1986 .

[3]  Janusz T. Starczewski,et al.  Connectionist Structures of Type 2 Fuzzy Inference Systems , 2001, PPAM.

[4]  T. Cacoullos.  Estimation of a multivariate density , 1966 .

[5]  Leszek Rutkowski,et al.  A general approach to neuro-fuzzy systems , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[6]  L. Rutkowski,et al.  A neuro-fuzzy controller with a compromise fuzzy reasoning , 2002 .

[7]  L. Rutkowski.  Sequential Estimates of a Regression Function by Orthogonal Series with Applications in Discrimination , 1981 .

[8]  L. Rutkowski.  Nonparametric identification of quasi-stationary systems , 1985 .

[9]  L. Rutkowski.  Application of multiple Fourier series to identification of multivariable non-stationary systems , 1989 .

[10]  W. Greblicki,et al.  An orthogonal series estimate of time-varying regression , 1983 .

[11]  Leszek Rutlowski.  Sequential pattern recognition procedures derived from multiple Fourier series , 1988 .

[12]  Krzysztof Patan,et al.  Optimal training strategies for locally recurrent neural networks , 2011 .

[13]  Ryszard Tadeusiewicz,et al.  Artificial Intelligence and Soft Computing - ICAISC 2006, 8th International Conference, Zakopane, Poland, June 25-29, 2006, Proceedings , 2006, International Conference on Artificial Intelligence and Soft Computing.

[14]  Leszek Rutkowski.  Nonparametric Procedures for Identification and Control of Linear Dynamic Systems , 1988 .

[15]  L. Rutkowski,et al.  Nonparametric recovery of multivariate functions with applications to system identification , 1985, Proceedings of the IEEE.

[16]  E. Rafajłowicz,et al.  On optimal global rate of convergence of some nonparametric identification procedures , 1989 .

[17]  Robert Cierniak,et al.  On image compression by competitive neural networks and optimal linear predictors , 2000, Signal Process. Image Commun..

[18]  Janusz T. Starczewski,et al.  Interval Type 2 Neuro-Fuzzy Systems Based on Interval Consequents , 2003 .

[19]  Leszek Rutkowski,et al.  On system identification by nonparametric function fitting , 1982 .

[20]  W. T. Federer,et al.  Stochastic Approximation and NonLinear Regression , 2003 .

[21]  P. J. Green,et al.  Probability and Statistical Inference , 1978 .

[22]  Leszek Rutkowski,et al.  Neural Networks and Soft Computing , 2003 .

[23]  J. K. Benedetti.  On the Nonparametric Estimation of Regression Functions , 1977 .

[24]  Leszek Rutkowski.  Multiple Fourier series procedures for extraction of nonlinear regressions from noisy data , 1993, IEEE Trans. Signal Process..

[25]  Robert Nowicki,et al.  Information Criterions Applied to Neuro-Fuzzy Architectures Design , 2004, ICAISC.

[26]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[27]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[28]  L. Rutkowski.  Non-parametric learning algorithms in time-varying environments☆ , 1989 .

[29]  Leszek Rutkowski,et al.  Identification of MISO nonlinear regressions in the presence of a wide class of disturbances , 1991, IEEE Trans. Inf. Theory.

[30]  L. Rutkowski.  On-line identification of time-varying systems by nonparametric techniques , 1982 .

[31]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[32]  Leszek Rutkowski,et al.  A new method for system modelling and pattern classification , 2004 .

[33]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[34]  W. Greblicki,et al.  Density-free Bayes risk consistency of nonparametric pattern recognition procedures , 1981, Proceedings of the IEEE.

[35]  Erwin Kreyszig,et al.  Introductory Mathematical Statistics. , 1970 .

[36]  Robert Nowicki.  Rough Sets in the Neuro-Fuzzy Architectures Based on Monotonic Fuzzy Implications , 2004, ICAISC.

[37]  Leszek Rutkowski.  On Bayes Risk Consistent Pattern Recognition Procedures in a Quasi-Stationary Environment , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  Adam Krzyzak,et al.  A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.

[39]  Leszek Rutkowski,et al.  A fast training algorithm for neural networks , 1998 .

[40]  Rafal Scherer.  Boosting Ensemble of Relational Neuro-fuzzy Systems , 2006, ICAISC.

[41]  Leszek Rutkowski,et al.  ORTHOGONAL SERIES ESTIMATES OF A REGRESSION FUNCTION WITH APPLICATIONS IN SYSTEM IDENTIFICATION , 1982 .

[42]  L. Rutkowski.  On nonparametric identification with prediction of time-varying systems , 1984 .

[43]  Ewaryst Rafaj⌈owicz.  Nonparametric orthogonal series estimators of regression: A class attaining the optimal convergence rate in L2☆ , 1987 .

[44]  L. Rutkowski.  Real-time identification of time-varying systems by non-parametric algorithms based on Parzen kernels , 1985 .

[45]  Jörg H. Siekmann,et al.  Artificial Intelligence and Soft Computing - ICAISC 2004 , 2004, Lecture Notes in Computer Science.