Structural learning of neurofuzzy GMDH with Minkowski norm

There have been many studies of mathematical models of neural networks. However, there always arises a problem of determining their optimal structures due to the lack of prior information. We propose a procedure for the structure clarification of neurofuzzy GMDH model whose building blocks are represented by the radial basis functions network. The proposed method prunes the unnecessary links and units from the larger network to identify, as well as to clarify the network structure by minimizing the Minkowski norm of the derivatives of the building blocks.

[1]  S. Ergezinger,et al.  An accelerated learning algorithm for multilayer perceptrons: optimization layer by layer , 1995, IEEE Trans. Neural Networks.

[2]  Itsuo Hatono,et al.  Extraction of Fuzzy Rules Using Fuzzy Neural Networks with Forgetting , 1996 .

[3]  Masumi Ishikawa,et al.  Prediction of time series by a structural learning of neural networks , 1996, Fuzzy Sets Syst..

[4]  Stanley J. Farlow,et al.  Self-Organizing Methods in Modeling: Gmdh Type Algorithms , 1984 .

[5]  Hidetomo Ichihashi,et al.  Successive Projection Method for Learning of Neurofuzzy GMDH , 1997 .

[6]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[7]  A. G. Ivakhnenko,et al.  Polynomial Theory of Complex Systems , 1971, IEEE Trans. Syst. Man Cybern..

[8]  T Poggio,et al.  Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks , 1990, Science.

[9]  Yann LeCun,et al.  Optimal Brain Damage , 1989, NIPS.

[10]  A. N. Mucciardi,et al.  Neuromine Nets as the Basis for the Predictive Component of Robot Brains , 1972 .

[11]  Hidetomo Ichihashi,et al.  Learning of Neurofuzzy GMDH by Successive Projection Method , 1996 .

[12]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[13]  Gregory J. Wolff,et al.  Optimal Brain Surgeon: Extensions and performance comparisons , 1993, NIPS 1993.

[14]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[15]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[16]  Martin Brown,et al.  Neurofuzzy adaptive modelling and control , 1994 .

[17]  Russell Reed,et al.  Pruning algorithms-a survey , 1993, IEEE Trans. Neural Networks.

[18]  Masumi Ishikawa,et al.  Structural learning with forgetting , 1996, Neural Networks.