SELF-ORGANIZING MAP AND ITS LEARNING IN THE FUZZY CLUSTERING-CLASSIFICATION TASKS

Bodyanskiy Ye., Vynokurova O., Mulesa P., Slipchenko O.
Abstract: 
In the paper, combined self-learning and learning method of self-organizing map (SOM-LVQ) is proposed. Such method allows to increase quality of information processing under condition of overlapping classes due to rational choice of learning rate parameter and introducing special procedure of fuzzy reasoning in the clustering-classification process, which occurs both with external learning signal (“supervised”), and without one (“unsupervised”). As similarity measure of neighborhood function or membership one, cosine structures are used, which allow to provide a high flexibility due to self-learning-learning process and to provide some new useful properties.
References: 

1. Kohonen, T. Self-Organizing Maps. – Berlin: Springer-Verlag, 1995 – 362 p. 2. Haykin, S. Neural Networks: A Comprehensive Foundation. - Upper Saddle River, N.Y.: Prentice Hall, 1999. – 842 p. 3. Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press, 1981. – 272 p. 4. Hoeppner, F., Klawon, T., Kruse, R. Fuzzy Clusteranalyse: Verfahren fuer die Belderkennung, Klassification und Datenanalyse. – Braunschweig: Vieweg, Reihe Computational Intelligence, 1996. – 280 S. 5. Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N. Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Springer, 1999 – 777 p. 6. Hoeppner F., Klawonn F., Kruse R., Runkler T. Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. - Chichester: John Wiley & Sons, 1999. – 300 p. 7. Sato-Ilic M., Jain L. Innovations in Fuzzy Clustering: Theory and Applications. – Berlin: Springer, 2006. – 152 p. 8. Vuorimaa, P. Use of the fuzzy self-organizing map in pattern recognition // Proc. 3-rd IEEE Int. Conf. Fuzzy Systems “FUZZ-IEEE’94”. - Orlando, USA, 1994 – P.798-801. 9. Vuorimaa, P. Fuzzy self-organizing map // Fuzzy Sets and Systems. - 1994. - 66. - P. 223-231. 10. Tsao E.C.-K., Bezdek J.C., Pal N.R. Fuzzy Kohonen clustering networks // Pattern recognition. – 1994. – 27. – P. 757-764. 11. Pascual-Marqui R.D., Pascual-Montano A.D., Kochi K., Caraso J.M. Smoothly distributed fuzzy C-means: a new self-organizing map // Pattern Recognition. – 2001. – 34. – P. 2395-2402. 12. Sepkovski, J.J. Quantified coefficients of association and measurement of simularity // J. Int. Ass. Math. - 1974. – 6 (2). – P. 135-152. 13. Wasan M.T. Stochastic Approximation. – Cambridge: The University Press, 2004. – 216 p. 14. Dvoretzky, A., On stochastic approximation // Proc. 3-rd Berkley Symp. Math. Statistics and Probability. – 1956. – 1. – P. 39-55. 15. Goodwin, G.C., Ramadge, P.J., Caines, P.E. A globally convergent adaptive predictor // Automatica. – 1981 – 17 (1). – P.135-140. 16. Grossberg S. Classical and instrumental learning by neural networks // In “Progress in Theoretical Biology”. – N.Y.: Academic Press, 1974. – 3 – P. 51-141. 17. Baras J.C., La Vigna A. Convergence of Kohonen's learning vector quantization // Proc. Int. Joint Conf. on Neural Networks. – San Diego, CA, 1990. – 3. – P.17-20.