Genetic Selection and Cloning in GMDH MIA Method. Marcel Jirina, Marcel Jirina, jr. IWIM, Prague, 2007.

 Article (in pdf)

Abstract. The GMDH MIA algorithm is modified by the use of selection procedure from genetic algorithms and including cloning of the best neurons generated to get even lesser error. The selection procedure finds parents for a new neuron among already existing neurons according to fitness and with some probability also from network inputs. The essence of cloning is slight modification of parameters of copies of the best neuron, i.e. neuron with the largest fitness. We describe the algorithm and show that the procedure is relatively simple. The genetically modified GMDH network with cloning (GMC-GMDH) can outperform other powerful methods. It is demonstrated on some tasks from Machine Learning Repository.

Keywords. Inductive modeling, GMDH MIA algorithm, genetic algorithm, genetic selection, cloning, artificial neural networks.

References.

1. Ivakhnenko, A.G.: Polynomial Theory of Complex System. IEEE Trans. on Systems, Man and Cybernetics, Vol. SMC-1, No. 4, Oct. 1971, pp. 364-378.
2. Farlow, S.J.: Self-Organizing Methods in Modelling. GMDH Type Algorithms. Marcel Dekker, Inc., New York, 1984.
3. Tamura, H., Kondo, T.: Heuristics-free group method of data handling algorithm of generating optimal partial polynomials with application to air pollution prediction. Int. J.Systems Sci., 1980, vol. 11, No. 9, pp. 1095-111. See also Farlow 1984 p. 225-241.
4. Ivakhnenko, A.G., Mller, J.A.: Present State and New Problems of Further GMDH Development. SAMS, Vol. 20, 1995, pp. 3-16.
5. Ivakhnenko, A.G., Ivakhnenko, G.A., Mller, J.A.: Self-Organization of Neural Networks with Active Neurons. Pattern Recognition and Image Analysis, Vol. 4, No. 2, 1994, pp. 177-188.
6. Ivakhnenko, A.G., Wunsch, D., Ivakhnenko, G.A.: Inductive Sorting/out GMDH Algorithms with Polynomial Complexity for Active neurons of Neural network. IEEE 6/99, 1999, pp. 1169-1173.
7. Nariman-Zadeh, N. et al.: Modelling of Explosive Cutting process of Plates using GMDH-type neural network and Singular value Decomposition. Journ. of material processes technology Vol. 128, 2002, No. 1-3, pp. 80-87.
8. Hiassat,M., Mort.N.: An evolutionary method for term selection in the Group Method of Data Handling. Automatic Control & Systems Engineering, University of Sheffield, www.maths.leeds.ac.uk/statistics/workshop/lasr2004/Proceedings/hiassat.pdf.
9. Oh, S.K., Pedrycz, W.: The Design of Self-organizing Polynomial Neural Networks. Information Sciences (Elsevier), Vol. 141, Apr. 2002, No. 3-4, pp 237-258.
10. F.Hakl, M.Jirina, E.Richter-Was: Hadronic tau’s identification using artificial neural network. ATLAS Physics Communication, ATL-COM-PHYS-2005-044, last revision: 26 August 2005,  http://documents.cern.ch/cgi-bin/setlink?base=atlnot&categ=Communication&id=com-phys-2005-044.
11. Negative Selection Algorithms> From the Thymus to V-Detector. Dissertation Presented for the Doctor of Philosophy Degrese. The University of Memphis, August, 2006.
12. Guney K., Akdagli A., Babayigit B.: Shaped-beam pattern synthesis of linear antenna arrays with the use of a clonal selection algorithm. Neural Network world, Volume 16 (2006), pp. 489-501.
13. Merz,C.J., Murphy,P.M., Aha,D.W.: UCI Repository of Machine Learning Databases. Dept. of Information and Computer Science, Univ. of California, Irvine,  http://www.ics.uci.edu/~mlearn/MLrepository.html, 1997.
14. R. Paredes, E. Vidal, Learning Weighted Metrics to Minimize Nearest-Neighbor Classification Error. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 7, July 2006, pp. 1100-1110.