Analysis of User-Weighted π Rough k-Means

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8818)


Since its introduction by Lingras and West a decade ago, rough k-means has gained increasing attention in academia as well as in practice. A recently introduced extension, π rough k-means, eliminates need for the weight parameter in rough k-means applying probabilities derived from Laplace’s Principle of Indifference. However, the proposal in its more general form makes it possible to optionally integrate user-defined weights for parameter tuning using techniques such as evolutionary computing. In this paper, we study the properties of this general user-weighted π k-means through extensive experiments.


Rough k-Means User-Defined Weights Soft Clustering 


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  1. 1.
    Bache, K., Lichman, M.: UCI machine learning repository (2013)Google Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Algorithms. Plenum Press, New York (1981)CrossRefMATHGoogle Scholar
  3. 3.
    Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recognition Letters 31, 651–666 (2010)CrossRefGoogle Scholar
  4. 4.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems 1(2), 98–110 (1993)CrossRefGoogle Scholar
  5. 5.
    Laplace, P.S.: Philosophical Essay on Probabilities. Dover Pub, New York (1951)MATHGoogle Scholar
  6. 6.
    Lingras, P.: Evolutionary rough K-means clustering. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 68–75. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Lingras, P., Peters, G.: Rough clustering. WIREs Data Mining and Knowledge Discovery 1, 64–72 (2011)CrossRefGoogle Scholar
  8. 8.
    Lingras, P., Peters, G.: Applying rough set concepts to clustering. In: Peters, G., Lingras, P., Ślęzak, D., Yao, Y.Y. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Advanced Information and Knowledge Processing, pp. 23–37. Springer, London (2012)Google Scholar
  9. 9.
    Lingras, P., West, C.: Interval set clustering of web users with rough k-means. Journal of Intelligent Information Systems 23, 5–16 (2004)CrossRefMATHGoogle Scholar
  10. 10.
    Lloyd, S.P.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28(2), 129–137 (1982)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Maji, P., Pal, S.K.: RFCM: A hybrid clustering algorithm using rough and fuzzy sets. Fundamenta Informaticae 80(4), 475–496 (2007)MathSciNetMATHGoogle Scholar
  12. 12.
    Maji, P., Pal, S.K.: Rough set based generalized fuzzy c-means algorithm and quantitative indices. IEEE Transactions on Systems, Man, and Cybernetics - Part B 37(6), 1529–1540 (2007)CrossRefGoogle Scholar
  13. 13.
    Maji, P., Paul, S.: Rough-fuzzy C-means for clustering microarray gene expression data. In: Kundu, M.K., Mitra, S., Mazumdar, D., Pal, S.K. (eds.) PerMIn 2012. LNCS, vol. 7143, pp. 203–210. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Mitra, S.: An evolutionary rough partitive clustering. Pattern Recognition Letters 25, 1439–1449 (2004)CrossRefGoogle Scholar
  15. 15.
    Mitra, S., Banka, H., Pedrycz, W.: Rough-fuzzy collaborative clustering. IEEE Transactions on Systems, Man, and Cybernetics - Part B 36(4), 795–805 (2006)CrossRefGoogle Scholar
  16. 16.
    Pal, S.K., Majumder, D.D.: Fuzzy sets and decision making approaches in vowel and speaker recognition. IEEE Transactions on Systems, Man, and Cybernetics 7, 625–629 (1977)CrossRefMATHGoogle Scholar
  17. 17.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Peters, G.: Some refinements of rough k-means. Pattern Recognition 39, 1481–1491 (2006)CrossRefMATHGoogle Scholar
  19. 19.
    Peters, G.: Rough clustering utilizing the principle of indifference. Information Sciences 277, 358–374 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Peters, G., Crespo, F., Lingras, P., Weber, R.: Soft clustering - fuzzy and rough approaches and their extensions and derivatives. International Journal of Approximate Reasoning 54(2), 307–322 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Peters, G., Lampart, M.: A partitive rough clustering algorithm. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 657–666. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Peters, G., Lampart, M., Weber, R.: Evolutionary rough k-medoid clustering. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 289–306. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 291–317 (1996)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Munich University of Applied Sciences, MunichGermany & Australian Catholic UniversitySydneyAustralia
  2. 2.Saint Mary’s UniversityHalifaxCanada

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