A Refined Rough k-Means Clustering with Hybrid Threshold

  • Hailiang Wang
  • Mingtian Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7413)


In this paper, we propose a new type of adaptive weight based on the definiteness of rough clusters and a hybrid threshold by combining the difference and distance threshold. And then, we refine the algorithm for assigning objects based on the hybrid thresholds to ensure that the outliers in inline positions and rectangle positions to be represented reasonably. At last, some experiments are provided to compare this refined RCM with the original RCM.


Rough sets Clustering Approximation Accuracy Hybrid Threshold 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hartigan, J.A., Wong, M.A.: A K-Means Clustering Algorithm. Journal of Applied Statistics 28, 100–108 (1979)zbMATHCrossRefGoogle Scholar
  2. 2.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ruspini, E.: A new approach to clustering. Inform. Control 15, 22–32 (1969)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybernet. 3, 32–57 (1974)MathSciNetGoogle Scholar
  5. 5.
    Bezdek, J.C.: Pattern Recognition With Fuzzy Objective Function Algorithm. Kluwer, New York (1981)CrossRefGoogle Scholar
  6. 6.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1(2), 98–110 (1993)CrossRefGoogle Scholar
  7. 7.
    Pal, N.R., Pal, K., Keller, J.M., Bezdek, J.C.: A possibilistic fuzzy c-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13(4), 517–530 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Pawlak, Z.: Rough Sets. International Journal of Information and Computer Sciences 11, 145–172 (1982)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pawlak, Z.: Some Issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Mitraa, S., Pedryczb, W., Barmanc, B.: Shadowed c-means: Integrating fuzzy and rough clustering. Pattern Recognition 43(4), 1282–1291 (2010)CrossRefGoogle Scholar
  11. 11.
    Zhou, T., Zhang, Y., Lu, H., Deng, F., Wang, F.: Rough Cluster Algorithm Based on Kernel Function. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 172–179. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Lingras, P., West, J.: Interval set clustering of web users with rough k-means. Journal of Intelligent Information Systems 23(1), 5–16 (2004)zbMATHCrossRefGoogle Scholar
  13. 13.
    Mitra, S., Banka, H., Pedrycz, W.: Rough-fuzzy collaborative clustering. IEEE Trans. Syst., Man, Cybern. B, Cybern. 36(4), 795–805 (2006)CrossRefGoogle Scholar
  14. 14.
    Maji, P., Pal, S.K.: RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets. Fundamenta Informaticae 80(4), 477–498 (2007)MathSciNetGoogle Scholar
  15. 15.
    Maji, P., Pal, S.K.: Rough Set Based Generalized Fuzzy C-Means Algorithm and Quantitative Indices. IEEE Trans. Systems, Man, and Cybernetics 37(6), 1529–1540 (2007)CrossRefGoogle Scholar
  16. 16.
    Yao, Y., Lingras, P., Wang, R., Miao, D.: Interval Set Cluster Analysis: A Re-formulation. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 398–405. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Zhou, T., Zhang, Y.N., Lu, H.L.: Rough k-means Cluster with Adaptive Parameters. In: 6th Int. Conf. Machine Learning and Cybernetics, Hong Kong, China, pp. 3063–3068 (2007)Google Scholar
  18. 18.
    Peters, G.: Outliers in Rough k-Means Clustering. In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds.) PReMI 2005. LNCS, vol. 3776, pp. 702–707. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Peters, G.: Some refinement of rough k-means clustering. Pattern Recognition 39, 1481–1491 (2006)zbMATHCrossRefGoogle Scholar
  20. 20.
    Mitra, S.: An evolutionary rough partitive clustering. Pattern Recognition Letters 25, 1439–1449 (2004)CrossRefGoogle Scholar
  21. 21.
    Pal, S.K., Shankar, B.U., Mitra, P.: Granular computing, rough entropy and object extraction. Pattern Recognition Letters 26, 2509–2517 (2005)CrossRefGoogle Scholar
  22. 22.
    Małyszko, D., Stepaniuk, J.: Rough Entropy Based k-Means Clustering. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 406–413. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hailiang Wang
    • 1
  • Mingtian Zhou
    • 1
  1. 1.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChenduP.R. China

Personalised recommendations