Function Approximation Using Robust Radial Basis Function Networks

Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical ro- bustness of a particular class of non-quadratic estimators known as M-estimators in Statistics and dead-zone. The al- gorithms is tested on some examples, and the results show that the proposed algorithm not only eliminates the influence of the outliers but has better convergence rate then the standard Gauss-Newton algorithm.

[1]  Rogelio Lozano,et al.  Reformulation of the parameter identification problem for systems with bounded disturbances , 1987, Autom..

[2]  LeeChien-Cheng,et al.  Noisy time series prediction using M-estimator based robust radial basis function neural networks with growing and pruning techniques , 2009 .

[3]  C. Harris,et al.  Advanced Adaptive Control , 1995 .

[4]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[5]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[6]  Shing-Chow Chan,et al.  A recursive least M-estimate algorithm for robust adaptive filtering in impulsive noise: fast algorithm and convergence performance analysis , 2004, IEEE Transactions on Signal Processing.

[7]  Qing Song,et al.  Pruning Based Robust Backpropagation Training Algorithm for RBF Network Tracking Controller , 2007, J. Intell. Robotic Syst..

[8]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[9]  P. Holland,et al.  Robust regression using iteratively reweighted least-squares , 1977 .

[10]  Abdelhak M. Zoubir,et al.  A sequential algorithm for robust parameter estimation , 2005, IEEE Signal Processing Letters.

[11]  J. Chambers,et al.  A robust mixed-norm adaptive filter algorithm , 1997, IEEE Signal Processing Letters.

[12]  D. Ruppert.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[13]  Stuart Geman,et al.  Statistical methods for tomographic image reconstruction , 1987 .

[14]  Carlos Canudas de Wit,et al.  A modified EW-RLS algorithm for systems with bounded disturbances , 1990, Autom..

[15]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[16]  Dennis Deng,et al.  Sequential and Adaptive Learning Algorithms for M-Estimation , 2008, EURASIP J. Adv. Signal Process..

[17]  Christos H. Papadimitriou,et al.  On the Value of Information , 1996 .

[18]  T. Ng,et al.  A recursive least M-estimate (RLM) adaptive filter for robust filtering in impulse noise , 2000, IEEE Signal Processing Letters.

[19]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[20]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[21]  Christopher M. Bishop,et al.  Neural Network for Pattern Recognition , 1995 .

[22]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[23]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[24]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[25]  Jin-Tsong Jeng,et al.  Annealing robust radial basis function networks for function approximation with outliers , 2004, Neurocomputing.

[26]  Chien-Cheng Lee,et al.  Noisy time series prediction using M-estimator based robust radial basis function neural networks with growing and pruning techniques , 2009, Expert Syst. Appl..