Weak Convergence of the Recursive Parzen-Type Probabilistic Neural Network in a Non-stationary Environment

A recursive version of general regression neural networks is presented. Weak convergence is proved in a case of nonstationary noise. Experimental results are given.

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

[2]  Charu C. Aggarwal,et al.  Data Streams: Models and Algorithms (Advances in Database Systems) , 2006 .

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

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

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

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

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

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

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

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

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

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

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

[14]  Charu C. Aggarwal,et al.  Data Streams - Models and Algorithms , 2014, Advances in Database Systems.

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

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

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

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

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

[20]  M. Abramson.  A Note on Permanents , 1971, Canadian Mathematical Bulletin.

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

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

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

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

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

[26]  I. Ahmad,et al.  NONPARAMETRIC SEQUENTIAL ESTIMATION OF A MULTIPLE REGRESSION FUNCTION , 1976 .

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

[28]  James Stephen Marron,et al.  Choosing a Kernel Regression Estimator , 1991 .

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

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

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

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

[34]  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.

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

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

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

[38]  Edward J. Wegman,et al.  Remarks on Some Recursive Estimators of a Probability Density , 1979 .

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

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

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

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

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