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Abstrakty
The paper deals with the problem of discovering fuzzy clusters with optimal number of elements in heuristic possibilistic clustering. The relational clustering procedure using a parameter that controls cluster sizes is considered and a technique for detecting the optimal number of elements in fuzzy clusters is proposed. The effectiveness of the proposed technique is illustrated through numerical examples. Experimental results are discussed and some preliminary conclusions are formulated.
Słowa kluczowe
Rocznik
Tom
Strony
45--76
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
- Department of Software Information Technology, Belarusian State University of Informatics and Radio-Electronics, P. Brovka St. 6, 220013 Minsk, Belarus
Bibliografia
- [1] Anderson E., The irises of the Gaspe Peninsula, Bulletin of the American Iris Society, 59, 1, 1935, 2-5.
- [2] Bezdek J.C., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981.
- [3] Chiang J.-H., Yue S., Yin Z.-X., A new fuzzy cover approach to clustering, IEEE Transactions on Fuzzy Systems, 12, 2, 2004, 199-208.
- [4] Corsini P., Lazzerini B., Marcelloni F., A new fuzzy relational clustering algorithm based on the fuzzy C-means algorithm, Soft Computing, 9, 6, 2005, 439-447.
- [5] De Cáceres M., Oliva F., Font X., On relational possibilistic clustering, Pattern Recognition, 39, 11, 2006, 2010-2024.
- [6] Everitt B.S., Landau S., Leese M., Stahl D., Cluster Analysis, 5th Edition, Wiley, Chichester, 2011.
- [7] Hamasuna Y., Endo Y., Miyamoto S., Fuzzy C-means clustering for data with clusterwise tolerance based on L2- and L1-regularization, Journal of Advanced Computational Intelligence and Intelligent Informatics, 15, 1, 2011, 68-75.
- [8] Höppner F., Klawonn F., Kruse R., Runkler T., Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition, John Wiley & Sons, Chichester, 1999.
- [9] Kaufmann A., Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975.
- [10] Komazaki Y., Miyamoto S., Variables for controlling cluster sizes on fuzzy C-means, in: V. Torra, Y. Narukawa, G. Navarro-Arribas, D. Megías (eds.), Modeling Decisions for Artificial Intelligence: Proceedings of the 10th International Conference MDAI’2013, Barcelona, Spain, November 20-22, 2013, Springer, Berlin, 2013, 192-203.
- [11] Krishnapuram R., Keller J.M., A possibilistic approach to clustering, IEEE Transactions on Fuzzy Systems, 1, 2, 1993, 98-110.
- [12] Łęski J.M., Robust possibilistic clustering, Archives of Control Sciences, 10, 3/4, 2000, 141-155.
- [13] Mandel I.D., Clustering Analysis, Finansy i Statistica, Moscow, 1988. (in Russian).
- [14] Ménard M., Courboulay V., Dardignac P.-A., Possibilistic and probabilistic fuzzy clustering: unification within the framework of the non-extensive thermostatistics, Pattern Recognition, 36, 6, 2003, 1325-1342.
- [15] Miyamoto S., Ichihashi H., Honda K., Algorithms for Fuzzy Clustering. Methods in C-Means Clustering with Applications, Springer, Berlin, 2008.
- [16] Miyamoto S., Different objective functions in fuzzy C-means algorithms and kernel-based clustering, International Journal of Fuzzy Systems, 13, 2, 2011, 89-97.
- [17] Pedrycz W., Fuzzy sets in pattern recognition: methodology and methods, Pattern Recognition, 23, 1/2, 1990, 121-146.
- [18] Sato-Ilic M., Jain L.C., Innovations in Fuzzy Clustering. Theory and Applications, Springer, Berlin, 2006.
- [19] Sneath P.H.A., Sokal R., Numerical Taxonomy, Freeman, San Francisco, 1973.
- [20] Tamura S., Higuchi S., Tanaka K., Pattern classification based on fuzzy relations, IEEE Transactions on Systems, Man, and Cybernetics, 1, 1, 1971, 61-66.
- [21] Vapnik V.N., Statistical Learning Theory, Wiley, New York, 1998.
- [22] Viattchenin D.A., A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications, Springer, Berlin, 2013.
- [23] Viattchenin D.A., Damaratski A., Direct heuristic algorithms of possibilistic clustering based on transitive approximation of fuzzy tolerance, Informatica Economicá Journal, 17, 3, 2013, 5-15.
- [24] Viattchenin D.A., Yaroma A., Damaratski A., A novel direct relational heuristic algorithm of possibilistic clustering, International Journal of Computer Applications, 107, 18, 2014, 15-21.
- [25] Walesiak M., Ugólniona Miara Odległości w Statystycznej Analizie Wielowymiarowej, Wydawnictwo Akademii Ekonomicznej im. Oskara Langego, Wrocław, 2002. (in Polish).
- [26] Xie Z., Wang S.T., Chung F.L., An enhanced possibilistic c-means clustering algorithm EPCM, Soft Computing, 12, 6, 2008, 593-611.
- [27] Yang M.-S., Wu K.-L., Unsupervised possibilistic clustering, Pattern Recognition, 39, 1, 2006, 5-21.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-44808c60-6778-4d61-ba8a-e7f7001c6fad