International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 9, No. 2, 8 Feb. 2017
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Fuzzy Clustering Data Given on the Ordinal Scale Based on Membership and Likelihood Functions Sharing
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Author(s)
Zhengbing Hu
1,*
Yevgeniy V. Bodyanskiy
2
Oleksii K. Tyshchenko
2
Viktoriia O. Samitova
2
Index Terms
Computational Intelligence, Machine Learning, ordinal data, FCM, membership function, likelihood function
Abstract
A task of clustering data given on the ordinal scale under conditions of overlapping clusters has been considered. It’s proposed to use an approach based on membership and likelihood functions sharing. A number of performed experiments proved effectiveness of the proposed method. The proposed method is characterized by robustness to outliers due to a way of ordering values while constructing membership functions.
Cite This Paper
Zhengbing Hu, Yevgeniy V. Bodyanskiy, Oleksii K. Tyshchenko, Viktoriia O. Samitova ,"Fuzzy Clustering Data Given on the Ordinal Scale Based on Membership and Likelihood Functions Sharing", International Journal of Intelligent Systems and Applications(IJISA), Vol.9, No.2, pp.1-9, 2017. DOI:10.5815/ijisa.2017.02.01
Reference
[1]R. Xu and D.C. Wunsch, Clustering. Hoboken, NJ: John Wiley & Sons, Inc. 2009.
[2]C.C. Aggarwal and C.K. Reddy, Data Clustering. Algorithms and Application. Boca Raton: CRC Press, 2014.
[3]Zh. Hu, Ye.V. Bodyanskiy, and O.K. Tyshchenko, “A Cascade Deep Neuro-Fuzzy System for High-Dimensional Online Possibilistic Fuzzy Clustering”, Proc. of the XI-th International Scientific and Technical Conference “Computer Science and Information Technologies” (CSIT 2016), 2016, Lviv, Ukraine, pp.119-122.
[4]Zh. Hu, Ye.V. Bodyanskiy, and O.K. Tyshchenko, “A Deep Cascade Neuro-Fuzzy System for High-Dimensional Online Fuzzy Clustering”, Proc. of the 2016 IEEE First Int. Conf. on Data Stream Mining & Processing (DSMP), 2016, Lviv, Ukraine, pp.318-322.
[5]Ye. Bodyanskiy, O. Tyshchenko, and D. Kopaliani, “An evolving neuro-fuzzy system for online fuzzy clustering”, Proc. Xth Int. Scientific and Technical Conf. “Computer Sciences and Information Technologies (CSIT’2015)”, 2015, pp.158-161.
[6]Ye. Bodyanskiy, O. Tyshchenko, and D. Kopaliani, “Adaptive learning of an evolving cascade neo-fuzzy system in data stream mining tasks”, in Evolving Systems, 2016, vol. 7(2), pp.107-116.
[7]Ye. Bodyanskiy, O. Tyshchenko, and D. Kopaliani, “An Extended Neo-Fuzzy Neuron and its Adaptive Learning Algorithm”, in I.J. Intelligent Systems and Applications (IJISA), 2015, vol.7(2), pp.21-26.
[8]Ye. Bodyanskiy, O. Tyshchenko, and D. Kopaliani, “A hybrid cascade neural network with an optimized pool in each cascade”, in Soft Computing. A Fusion of Foundations, Methodologies and Applications (Soft Comput), 2015, vol. 19(12), pp.3445-3454.
[9]Zh. Hu, Ye.V. Bodyanskiy, O.K. Tyshchenko, and O.O. Boiko, “An Evolving Cascade System Based on a Set of Neo-Fuzzy Nodes”, in International Journal of Intelligent Systems and Applications (IJISA), vol. 8(9), 2016, pp.1-7.
[10]Zhengbing Hu, Yevgeniy V. Bodyanskiy, O.K. Tyshchenko, Viktoriia O. Samitova,"Fuzzy Clustering Data Given in the Ordinal Scale", International Journal of Intelligent Systems and Applications(IJISA), Vol.9, No.1, pp.67-74, 2017. DOI: 10.5815/ijisa.2017.01.07.
[11]O. Tyshchenko, “A Reservoir Radial-Basis Function Neural Network in Prediction Tasks”, Automatic Control and Computer Sciences, Vol. 50, No. 2, pp. 65-71, 2016.
[12]Ye. Bodyanskiy, O. Tyshchenko, A. Deineko, “An Evolving Radial Basis Neural Network with Adaptive Learning of Its Parameters and Architecture”, Automatic Control and Computer Sciences, Vol. 49, No. 5, pp. 255-260, 2015.
[13]Z.B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations”, Proc. of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1967, pp.281-297.
[14]Lloyd S. P., Least Squares Quantization in PCM // IEEE Transactions on Information Theory. – 1982. – vol. IT-28. – P. 129-137.
[15]Bezdek J.C., Pattern Recognition with Fuzzy Objective Function Algorithms. – N.Y.:Plenum Press, 1981. – 272p.
[16]Jang J.-Sh. R., Sun Ch.-T., Mizutani E., Neuro-Fuzzy and Soft Computing. – Upper Saddle River, NJ: Prentice Hall, 1997. - 614 p.
[17]Dempster A. P., Laird N. M., and R. D. B., Maximum-Likelihood from Incomplete Data via the EM Algorithm // Journal of the Royal Statistical Society. – 1977. – vol.B. – P. 1-38
[18]Zhong S. and Ghosh J., A Unified Framework for Model-based Clustering // Journal of Machine Learning Research. – 2003. – vol. 4. – P. 1001-1037.
[19]M. Lee and R. K. Brouwer, “Likelihood Based Fuzzy Clustering for Data Sets of Mixed Features”, IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), 2007, pp.544-549.
[20]L. Mahnhoon, “Mapping of Ordinal Feature Values to Numerical Values through Fuzzy Clustering”, in IEEE Trans. on Fuzzy Systems, 2008, pp.732-737.
[21]Brouwer R.K., Pedrycz W. A feedforward neural network for mapping vectors to fuzzy sets of vectors // Proc.Int.Conf. on Artificial Neural Networks and Neural Information Processing ICANN/ICOMIP 2003. – Istanbul, Turkey, 2003. – P.45-48.
[22]B.S. Butkiewicz, “Robust fuzzy clustering with fuzzy data”, in Lecture Notes in Computer Science, Vol. 3528, 2005, pp.76-82.
[23]R.K. Brouwer, “Fuzzy set covering of a set of ordinal attributes without parameter sharing”, in Fuzzy Sets and Systems, 2006, vol. 157(13), pp.1775-1786.
[24]Ye.V. Bodyanskiy, V.A. Opanasenko, and А.N. Slipchenko, “Fuzzy clustering for ordinal data”, in Systemy Obrobky Informacii, 2007, Iss. 4(62), pp.5-9. (in Russian)
[25]F. Hoeppner, F. Klawonn, R. Kruse, and T. Runkler, Fuzzy Clustering Analysis: Methods for Classification, Data Analysis and Image Recognition. Chichester: John Wiley & Sons, 1999.