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Abstract

In this work we propose a clustering methodology model named as Mixture of Fuzzy Models (MFMs). We adopt two assumptions: the data points are generated by a membership function and the sum of the memberships to all of the clusters must be greater or equal than zero. The objective is to obtain a set of membership functions which represent the data. It is formulated as a multiobjective optimization problem with two objectives: to maximize the sum of memberships within each cluster and to maximize the differences of memberships between clusters.

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References

  1. Bezdek, J.C.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum, New York (1981)

    Book  MATH  Google Scholar 

  2. Chatzis, S.P., Tsechpenakis, G.: A possibilistic clustering approach toward generative mixture models. Pattern Recognition 45, 1819–1825 (2012)

    Article  MATH  Google Scholar 

  3. Chen, M.Y., Linkens, D.A.: Rule-base self-generation and simplification for data-driven fuzzy models. Fuzzy Sets and Systems 142, 243–265 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  5. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39, 1–38 (1977)

    MATH  MathSciNet  Google Scholar 

  6. Gan, M.T., Hanmandlu, M., Tan, A.H.: From a Gaussian mixture model to additive fuzzy systems. IEEE Transactions on Fuzzy Systems 13(3), 303–316 (2005)

    Article  Google Scholar 

  7. Ichihashi, H., Honda, K., Tani, N.: Gaussian mixture pdf approximation and fuzzy c-means clustering with entropy regularization. In: Proceedings of the Fourth Asian Fuzzy System Symposium, pp. 217–221 (2000)

    Google Scholar 

  8. Ju, Z., Liu, H.: Fuzzy Gaussian Mixture Models. Pattern Recognition 45, 1146–1158 (2012)

    Article  MATH  Google Scholar 

  9. McLachlan, G., Peel, D.: Finite Mixture Models. John Wiley & Sons, Inc. (2000)

    Google Scholar 

  10. Pal, N., Pal, K., Keller, J., Bezdek, J.: A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy Systems 13(4), 517–530 (2005)

    Article  MathSciNet  Google Scholar 

  11. Ruspini, E.H.: Numerical Methods for Fuzzy Clustering. Information Sciences (2), 319–350 (1970)

    Google Scholar 

  12. Sibson, R.: SLINK: an optimally efficient algorithm for the single-link cluster method. The Computer Journal (British Computer Society) 16(1), 30–34 (1973)

    MathSciNet  Google Scholar 

  13. Wu, K.L., Yang, M.S.: A cluster validity index for fuzzy clustering. Pattern Recognition Letters 26, 1275–1291 (2005)

    Article  Google Scholar 

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Pagola, M., Barrenechea, E., Jurío, A., Paternain, D., Bustince, H. (2014). Clustering Based on a Mixture of Fuzzy Models Approach. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-08855-6_48

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  • DOI: https://doi.org/10.1007/978-3-319-08855-6_48

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08854-9

  • Online ISBN: 978-3-319-08855-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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