Fuzzy Clustering Data Given on the Ordinal Scale Based on Membership and Likelihood Functions Sharing

Автор: Zhengbing Hu, Yevgeniy V. Bodyanskiy, Oleksii K. Tyshchenko, Viktoriia O. Samitova

Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa

Статья в выпуске: 2, 2017 года.

Бесплатный доступ

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.

Computational Intelligence, Machine Learning, ordinal data, FCM, membership function, likelihood function

Короткий адрес: https://sciup.org/15010079

IDR: 15010079

Список литературы Fuzzy Clustering Data Given on the Ordinal Scale Based on Membership and Likelihood Functions Sharing

  • R. Xu and D.C. Wunsch, Clustering. Hoboken, NJ: John Wiley & Sons, Inc. 2009.
  • C.C. Aggarwal and C.K. Reddy, Data Clustering. Algorithms and Application. Boca Raton: CRC Press, 2014.
  • Zhengbing 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.
  • Zhengbing 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.
  • 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.
  • 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.
  • Yevgeniy V. Bodyanskiy, O.K. Tyshchenko, Daria S. Kopaliani,"An Extended Neo-Fuzzy Neuron and its Adaptive Learning Algorithm", IJISA, Vol.7, No.2, pp.21-26, 2015. DOI: 10.5815/ijisa.2015.02.03.
  • 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.
  • Zhengbing Hu, Yevgeniy V. Bodyanskiy, O.K. Tyshchenko, Olena O. Boiko,"An Evolving Cascade System Based on a Set of Neo - Fuzzy Nodes", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.9, pp.1-7, 2016. DOI: 10.5815/ijisa.2016.09.01.
  • 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.
  • 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.
  • 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.
  • 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.
  • Lloyd S. P., Least Squares Quantization in PCM // IEEE Transactions on Information Theory. – 1982. – vol. IT-28. – P. 129-137.
  • Bezdek J.C., Pattern Recognition with Fuzzy Objective Function Algorithms. – N.Y.:Plenum Press, 1981. – 272p.
  • Jang J.-Sh. R., Sun Ch.-T., Mizutani E., Neuro-Fuzzy and Soft Computing. – Upper Saddle River, NJ: Prentice Hall, 1997. - 614 p.
  • 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
  • Zhong S. and Ghosh J., A Unified Framework for Model-based Clustering // Journal of Machine Learning Research. – 2003. – vol. 4. – P. 1001-1037.
  • 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.
  • L. Mahnhoon, "Mapping of Ordinal Feature Values to Numerical Values through Fuzzy Clustering", in IEEE Trans. on Fuzzy Systems, 2008, pp.732-737.
  • 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.
  • B.S. Butkiewicz, "Robust fuzzy clustering with fuzzy data", in Lecture Notes in Computer Science, Vol. 3528, 2005, pp.76-82.
  • 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.
  • 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)
  • 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.
Еще
Статья научная