Optimal Clustering with Twofold Memberships

  • Sadaaki Miyamoto
  • Jong Moon Choi
  • Yasunori Endo
  • Van Nam Huynh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)


This paper proposes two clustering algorithms of twofold memberships for each cluster. One uses a membership similar to that in K-means, while another membership is defined for a core of a cluster, which is compared to the lower approximation of a cluster in rough K-means. Two ideas for the lower approximation are proposed in this paper: one uses a neighborhood of a cluster boundary and another uses a simple circle from a cluster center. By using the two memberships, two alternate optimization algorithms are proposed. Numerical examples show the effectiveness of the proposed algorithms.


Neighborhood Clustering K-means Rough K-means Twofold memberships 



This paper is based upon work supported in part by the Air Force Office of Scientific Research/Asian Office of Aerospace Research and Development (AFOSR/AOARD) under award number FA2386-17-1-4046.


  1. 1.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer, Alphen aan den Rijn (1981)CrossRefGoogle Scholar
  2. 2.
    Dave, R.N.: Characterization and detection of noise in clustering. Pattern Recog. Lett. 12(11), 657–664 (1991)CrossRefGoogle Scholar
  3. 3.
    Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)CrossRefGoogle Scholar
  4. 4.
    Kinoshita, N., Endo, Y., Miyamoto, S.: On some models of objective-based rough clustering. In: Proceedings of 2014 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technologies, 11–14 August 2014, Warsaw, Poland (2014)Google Scholar
  5. 5.
    Kohonen, T.: Self-organizing Maps. Springer, Heidelberg (1995). Scholar
  6. 6.
    Lingras, P., West, C.: Interval set clustering of web users with rough k-means. J. Intell. Inf. Syst. 23, 5–16 (2004)CrossRefGoogle Scholar
  7. 7.
    MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)Google Scholar
  8. 8.
    Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Springer, Heidelberg (2008). Scholar
  9. 9.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  10. 10.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336), 846–850 (1971)CrossRefGoogle Scholar
  11. 11.
    Ubukata, S., Notsu, A., Honda, K.: The rough set \(k\)-means clustering. In: Proceedings of SCIS-ISIS, pp. 189–193 (2016)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sadaaki Miyamoto
    • 1
  • Jong Moon Choi
    • 1
  • Yasunori Endo
    • 1
  • Van Nam Huynh
    • 2
  1. 1.University of TsukubaTsukubaJapan
  2. 2.Japan Advanced Institute of Science and TechnologyNomiJapan

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