Abstract
A combined learning algorithm for a self-organizing map (SOM) is proposed. The algorithm accelerates information processing due to the rational choice of the learning rate parameter, and can work when the number of clusters is unknown, as well as when the clusters are overlapping. This is achieved via the introduction of fuzzy inference that determines the level of membership of the classified pattern to each of the available classes. For neighborhood and membership functions, raised cosine is used. This function provides more flexibility and some new properties for the self-learning and clustering procedures.
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References
T. Kohonen. Self-Organizing Maps. Springer-Verlag, Berlin, 1995.
J. C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, N.Y., 1981.
P. Vuorimaa. Fuzzy self-organizing maps. Fuzzy Sets and Systems, 66:223–231, 1994.
P. Vuorimaa. Use of the fuzzy self-organizing maps in pattern recognition. In Proc. 3-rd IEEE Int. Conf. Fuzzy Systems “FUZZ-IEEE’94”, pages 798–801, Orlando, USA, 1994.
E. C.-K. Tsao, J. C. Bezdek, and N. R. Pal. Fuzzy kohonen clustering networks. Pattern Recognition, 27:757–764, 1994.
R. D. Pascual-Marqui, A. D. Pascual-Montano, K. Kochi, and J. M. Caraso. Smoothly distributed fuzzy c-means: a new self-organizing map. Pattern Recognition, 34:2395–2402, 2001.
S. Haykin. Neural Networks. A Comprehensive Foundation. Prentice Hall, Inc., Upper Saddle River, N.Y., 1999.
A. Dvoretzky. On stochastic approximation. In Proc. 3-rd Berkeley Symp. Math. Statistics and Probability, volume 1, pages 39–55. University of California Press, 1956.
Ye. V. Bodyanskiy, I. P. Pliss, and T. V. Solovyova. Multistep optimal predictors for multi-variate non-stationary stochastic processes. Dokl. AN USSR, (12):47–49, 1986.
G. C. Goodwin, P. J. Ramadge, and P. E. Caines. A globally convergent adaptive predictor. Automatica, 17(1):135–140, 1981.
M. Cottrel and J. Fort. A stochastic model of retinotopy: a self-organizing process. Biological Cybernetics, 53:405–411, 1986.
H. Ritter and K. Shulten. On the stationary state of the Kohonen self-organizing sensory mapping. Biological Cybernetics, 54:234–249, 1986.
H. Ritter and K. Shulten. Covergence properties of Kohonen’s topology conserving maps: fluctuations, stability, and climension selection. Biological Cybernetics, 60:59–71, 1988.
R. J. Schilling, J. J. Carroll, and A. F. Al-Ajlouni. Approximation of nonlinear systems with radial basis function neural networks. IEEE Trans. on Neural Networks, 12(1):1–15, 2001.
S. Grossberg. Classical and instrumental learning by neural networks. In Proc. “Progress in Theoretical Biology”, volume 3, pages 57–141, N.Y., 1974. Academic Press.
Ye. Bodyanskiy, O. Chaplanov, V. Kolodyazhniy, and P. Otto. Adaptive quadratic radial basis function network for time series forecasting. In Proc. East West Fuzzy Coll. 2002, 10-th Zittau Fuzzy Coll., pages 164–172, Zittau/Goerlitz, 2002. HS.
Ye. Bodyanskiy, Ye. Gorshkov, V. Kolodyazhniy, and J. Wernstedt. Probabilistic neuro-fuzzy network with nonconventional activation functions. Lecture Notes in Artificial Intelligence, v.2773:973–979, 2003.
Ye. Bodyanskiy, Ye. Gorshkov, and V. Kolodyazhniy. Resource-allocating probabilistic neuro-fuzzy network. In Proc. Third Conf. of the European Society for Fuzzy Logic and Technology (EUSFLAT-2003), 10–12 September, 2003, pages 392–395, Zittau, Germany, 2003.
P. M. Murphy and D. W. Aha. UCI Repository of machine learning databases. University of California, Department of Information and Computer Science, CA, 1994.
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Bodyanskiy, Y., Gorshkov, Y., Kolodyazhniy, V., Stephan, A. (2005). Combined Learning Algorithm for a Self-Organizing Map with Fuzzy Inference. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_59
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DOI: https://doi.org/10.1007/3-540-31182-3_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22807-3
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