On the regularisation-enhanced training of RBF networks

The radial basis functions (RBF) network is important in neuro-fuzzy systems. In particular, their common universal approximator properties make fuzzy systems as well as neural network systems excellent representations for system modelling. In data-based modelling it is important that the overfitting should be avoided to enhance the generalisation capability of the model since this is an ultimate performance measure for the validity of the model. In this respect, in the majority of the reported researches with RBF networks, the issue of overfitting is omitted and it is attempted to make modelling errors vanish at the price of hidden degradation in generalisation properties of the network. The work addresses this issue in the RBF neural networks for enhanced neuro-fuzzy system modelling.

[1]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[2]  S. Billings,et al.  Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks , 1996 .

[3]  Sheng Chen,et al.  Practical identification of NARMAX models using radial basis functions , 1990 .

[4]  Ke Zeng,et al.  A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators , 2000, IEEE Trans. Fuzzy Syst..

[5]  Magne Setnes.  COMPLEXITY REDUCTION METHODS FOR FUZZY SYSTEMS DESIGN , 1999 .

[6]  David G. Stork,et al.  Pattern Classification , 1973 .

[7]  Mohamad T. Musavi,et al.  On the training of radial basis function classifiers , 1992, Neural Networks.

[8]  Özer Ciftcioglu,et al.  Knowledge management by information mining , 2001 .

[9]  Bart Kosko,et al.  Fuzzy Systems as Universal Approximators , 1994, IEEE Trans. Computers.

[10]  J. Yen,et al.  Simplification of fuzzy rule based systems using orthogonal transformation , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[11]  Stephen A. Billings,et al.  Radial basis function network configuration using genetic algorithms , 1995, Neural Networks.

[12]  W. Light.  Some Aspects of Radial Basis Function Approximation , 1992 .

[13]  Chuen-Tsai Sun,et al.  Functional equivalence between radial basis function networks and fuzzy inference systems , 1993, IEEE Trans. Neural Networks.

[14]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[15]  Roderick Murray-Smith,et al.  Extending the functional equivalence of radial basis function networks and fuzzy inference systems , 1996, IEEE Trans. Neural Networks.

[16]  C. Micchelli.  Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[17]  Dingli Yu,et al.  Selecting radial basis function network centers with recursive orthogonal least squares training , 2000, IEEE Trans. Neural Networks Learn. Syst..