Semi-Supervised Hard and Fuzzy c-Means with Assignment Prototype Term

  • Yukihiro Hamasuna
  • Yasunori Endo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8825)


Semi-supervised learning is an important task in the field of data mining. Pairwise constraints such as must-link and cannot-link are used in order to improve clustering properties. This paper proposes a new type of semi-supervised hard and fuzzy c-means clustering with assignment prototype term. The assignment prototype term is based on the Windham’s assignment prototype algorithm which handles pairwise constraints between objects in the proposed method. First, an optimization problem of the proposed method is formulated. Next, a new clustering algorithm is constructed based on the above discussions. Moreover, the effectiveness of the proposed method is shown through numerical experiments.


pairwise constraint hard c-means fuzzy c-means assignment prototype algorithm semi-supervised learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basu, S., Davidson, I., Wagstaff, K. (eds.): Constrained Clustering: Advances in Algorithms, Theory and Applications. Data Mining and Knowledge Discovery, vol. 3. Chapman & Hall/CRC (2008)Google Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chapelle, O., Schoölkopf, B., Zien, A. (eds.): Semi-Supervised Learning. MIT Press (2006)Google Scholar
  4. 4.
    Endo, Y.: On Entropy Based Fuzzy Non Metric Model – Proposal, Kernelization and Pairwise Constraints. Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII) 16(1), 169–173 (2012)Google Scholar
  5. 5.
    Hamasuna, Y., Endo, Y.: On semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria. Soft Computing 17(1), 71–81 (2013)CrossRefGoogle Scholar
  6. 6.
    Jain, A.K.: Data clustering: 50 years beyond K-means. Pattern Recognition Letters 31(8), 651–666 (2010)CrossRefGoogle Scholar
  7. 7.
    Klein, D., Kamvar, S., Manning, C.: From instance-level constraints to space-level constraints: making the most of prior knowledge in data clustering. In: Proc. of the 19th International Conference on Machine Learning (ICML 2002), pp. 307–314 (2002)Google Scholar
  8. 8.
    Kulis, B., Basu, S., Dhillon, I., Mooney, R.: Semi-supervised graph clustering: a kernel approach. Machine Learning 74(1), 1–22 (2009)CrossRefGoogle Scholar
  9. 9.
    MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proc. of Fifth Berkeley Symp. on Math. Statist. and Prob., pp. 281–297 (1967)Google Scholar
  10. 10.
    Miyamoto, S., Mukaidono, M.: Fuzzy c-means as a regularization and maximum entropy approach. In: Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA 1997), vol. 2, pp. 86–92 (1997)Google Scholar
  11. 11.
    Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  12. 12.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)CrossRefGoogle Scholar
  13. 13.
    Roubens, M.: Pattern classification problems and fuzzy sets. Fuzzy Sets and Systems 1, 239–253 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wagstaff, K., Cardie, C., Rogers, S., Schroedl, S.: Constrained k-means clustering with background knowledge. In: Proc. of the 18th International Conference on Machine Learning (ICML 2001), pp. 577–584 (2001)Google Scholar
  15. 15.
    Windham, M.P.: Numerical classification of proximity data with assignment measures. J. of Classification 2, 157–172 (1985)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yukihiro Hamasuna
    • 1
  • Yasunori Endo
    • 2
  1. 1.Department of Informatics, School of Science and EngineeringKinki UniversityHigashi-osakaJapan
  2. 2.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan

Personalised recommendations