Abstract:

Abstract Context. A task of data classification under conditions of clusters’ overlapping is considered in this article. Besides that, it’s assumed that information to be processed is given in the rank scale. Objective. It’s proposed to use a double neo-fuzzy neuron for classification which is a modification of a traditional neo-fuzzy neuron with specially designed asymmetrical membership functions and improved approximating properties. Method. The double neo-fuzzy neuron (just like the traditional one) is designated for processing data given the scale of natural numbers. However, the situation may become complicated greatly if source data is not given in the numerical scale but in the ordinal one which is a quite common case for a wide variety of practical tasks. Results. A gradient minimization procedure with a variable learning step parameter was used for learning the double neo-fuzzy neuron. The proposed approach to fuzzy classification for data given in the ordinal scale based on the double neo-fuzzy neuron which is learnt with the help of a high-speed algorithm possesses additional smoothing properties. The clustering accuracy for a training sample and the test one as well as the system’s learning speed were measured during experiments. The proposed architecture of the double neo-fuzzy neuron is a sort of compromise between a traditional neo-fuzzy neuron and its extended modification. This architecture demonstrates good performance in those cases when the results’ accuracy has more influence compared to the elapsed time used for data processing. Conclusions. Experimental implementation (for both artificial and real-world data) proved efficiency of the proposed techniques. During the experiments, properties of the proposed system were studied which confirmed usability of the proposed system for a wide range of Data Mining tasks. References Bezdek J. C. Pattern Recognition with Fuzzy Objective Function Algorithms / J. C. Bezdek. – N.Y. : Plenum Press, 1981. – 272 p. 2. Jang J.-Sh. R. Neuro-Fuzzy and Soft Computing / J.-Sh. R. Jang, Ch.-T. Sun, E. Mizutani. – Upper Saddle River, NJ : Prentice Hall, 1997. – 614 p. 3. Hoeppner F. Fuzzy Cluster Analyse / F. Hoeppner, F. Klawonn, R. Kruse. – Braunschweig : Vieweg, 1999. – 280 p. 4. Nelles O. Nonlinear System Identification / O. Nelles. – Berlin : Springer, 2001. – 785 p. 5. A neo-fuzzy neuron and its applications to system identification and prediction of the system behavior / [T. Yamakawa, E. Uchino, T. Miki, H. Kusanagi] // IIZUKA – 92: 2nd Int. Conf. on Fuzzy Logic and Neural Networks, Iizuka, Japan, 1992 : proceedings. – P. 477–483. 6. Miki T. Analog implementation of neo-fuzzy neuron and its onboarding learning / T. Miki, T. Yamakawa // Ed. by N. S. Mastorakis «Computational Intelligence and Application». – Piraeus : WSES Press, 1999. – P. 144–149. 7. Evolving network based on double neo-fuzzy neurons / [Ye. Bodyanskiy, Ye. Gorshkov, V. Kolodyazhniy, P. Otto] // Computer Science Meets Automation : 52nd Int. Scientific Coll., TU Ilmenau (Thuer), 2007: proceedings. – P. 35–40. 8. Brouwer R. K. Fuzzy Relational Fixed Point Clustering / R. K. Brouwer // International Journal of Computational Intelligence Systems. – 2009. – Vol. 2, Iss.1. – P. 69–82. 9. Brouwer R. K. Clustering feature vectors with mixed numerical and categorical attributes / R. K. Brouwer // International Journal of Computational Intelligence Systems. – 2008. – Vol. 1, Iss. 4. – P. 285–298. 10. Brouwer R. K. Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization / R. K. Brouwer, A. Groenwold // Soft Computing. – 2009. – Vol. 13, Iss. 6. – P. 577–589.

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