Optimised Information Abstraction in Granular Min/Max Clustering

  • Andrzej Bargiela
  • Witold Pedrycz
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 13)


The Min/Max classification and clustering has a distinct advantage of generating easily interpretable information granules - represented as hyperboxes in the multi-dimensional feature space of the data. However, while such an information abstraction lends itself to easy interpretation it leaves open the question whether the granules represent well the original data.

In this chapter we discuss an approach to optimised information abstraction, which retains the advantages of Min/Max clustering while providing a basis for building a more representative set of granules. In particular we extend the information density based granulation by including an extra stage of optimised refinement of granular prototypes. The initial granulation is accomplished by creating hyperboxes in the pattern space through the maximisation of the count of data items per unit volume of hyperboxes. The granulation is totally data driven in that it does not make any assumptions about the number or the maximum size of hyperboxes. Subsequent optimisation involves identification of granular prototypes and their refinement so as to achieve full reconstruction of the original data from the prototypes and the corresponding partition matrix.


Particle Swarm Optimisation Data Item Pattern Space Information Granule Granular Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Dordrecht (2003)zbMATHGoogle Scholar
  2. 2.
    Bargiela, A., Pedrycz, W.: Recursive information granulation: Aggregation and interpretation issues. IEEE Trans. on Syst. Man and Cybernetics 33(1), 96–112 (2003)CrossRefGoogle Scholar
  3. 3.
    Bargiela, A., Pedrycz, W.: Granular mappings. IEEE Transactions on Systems, Man, and Cybernetics-part A 35(2), 292–297 (2005)CrossRefGoogle Scholar
  4. 4.
    Bargiela, A., Pedrycz, W.: A model of granular data: a design problem with the Tchebyschev FCM. Soft Computing 9, 155–163 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bargiela, A., Pedrycz, W.: Toward a theory of Granular Computing for human-centered information processing. IEEE Transactions on Fuzzy Systems 16(2), 320–330 (2008)CrossRefGoogle Scholar
  6. 6.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, N. York (1981)zbMATHCrossRefGoogle Scholar
  7. 7.
    Chiu, S.: Method and software for extracting fuzzy classification rules by subtractive clustering. In: NAFIPS, pp. 461–465 (1996)Google Scholar
  8. 8.
    Cios, K., Pedrycz, W., Swiniarski, R.: Data Mining Techniques. Kluwer Academic Publishers, Boston (1998)Google Scholar
  9. 9.
    Gabrys, B., Bargiela, A.: General fuzzy min-max neural network for clustering and classification. IEEE Trans. on Neural Networks 11(3), 769–783 (2000)CrossRefGoogle Scholar
  10. 10.
    Hata, Y., Mukaidono, M.: On some classes of fuzzy information granularity and their representations. In: ISMVL 1999, Japan, pp. 288–293 (1999)Google Scholar
  11. 11.
    Kandel, A.: Fuzzy Mathematical Techniques with Applications. Addison-Wesley, Reading, MA (1986)zbMATHGoogle Scholar
  12. 12.
    Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. Int. J. General Systems 30, 33–154 (2001)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kacprzyk, J., Zadrozny: Linguistic database summaries and their protoforms: toward natural language based knowledge discovery tools. Information Sciences 173, 281–304 (2005)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ling, S.H., Iu, H.H.C., Chan, K.Y., Lam, H.K., Yeung, B.C.W., Leung, F.H.: Hybrid Particle Swarm Optimization with wavelet mutation and its industrial applications. IEEE Transactions on Systems, Man, and Cybernetics, Part B 38(3), 743–763 (2008)CrossRefGoogle Scholar
  15. 15.
    Moore, R.E.: Interval Analysis. Prentice Hall, Englewood Cliffs (1966)zbMATHGoogle Scholar
  16. 16.
    Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1998)zbMATHGoogle Scholar
  17. 17.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic, Dordrecht (1991)zbMATHGoogle Scholar
  18. 18.
    Pedrycz, W.: Computational Intelligence: An Introduction. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  19. 19.
    Pedrycz, W., Gomide, F.: An Introduction to Fuzzy Sets. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  20. 20.
    Pedrycz, W., Bargiela, A.: Information granulation: A search for data structures. In: Knowledge-based Engineering Systems KES 2001, Osaka, pp. 1147–1151 (October 2001)Google Scholar
  21. 21.
    Pedrycz, W., Valente de Oliveira, J.: A development of fuzzy encoding and decoding through fuzzy clustering. IEEE Transactions on Instrumentation and Measurement 57(4), 829–837 (2008)CrossRefGoogle Scholar
  22. 22.
    Pedrycz, W.: Knowledge-Based Fuzzy Clustering. John Wiley, N. York (2005)CrossRefGoogle Scholar
  23. 23.
    Simpson, P.K.: Fuzzy min-max neural networks. IEEE Transactions on Neural Networks 3, 776–786 (1992)CrossRefGoogle Scholar
  24. 24.
    Van den Bergh, F., Engelbrecht, A.P.: A study of particle swarm optimization particle trajectories. Information Sciences 176(8), 937–971 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North Holland, Amsterdam (1979)Google Scholar
  26. 26.
    Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 111–117 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Zadeh, L.A.: From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions. IEEE Trans. on Circuits and Systems 45, 105–119 (1999)MathSciNetGoogle Scholar
  28. 28.
    Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) – an outline. Information Sciences 172(1-2), 1–40 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Zhan, Z., Zhang, J., Li, Y., Chung, H.S.H.: Adaptive Particle Swarm optimization. IEEE Trans. on Systems, Man, and Cybernetics, Part B 39(6), 1362–1381 (2009)CrossRefGoogle Scholar
  30. 30.
    Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent Systems 16(1), 87–104 (2001)zbMATHCrossRefGoogle Scholar
  31. 31.
    Yao, Y.: A unified framework of granular computing. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 401–410. Wiley-Interscience, New York (2008)CrossRefGoogle Scholar
  32. 32.
    Yao, Y.Y.: Integrative levels of granularity. In: Bargiela, A., Pedrycz, W. (eds.) Human Centric Information Processing Through Granular Modelling, pp. 31–47. Springer, Berlin (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of NottinghamNottinghamUK
  2. 2.University of AlbertaEdmontonCanada

Personalised recommendations