Some Pairwise Constrained Semi-Supervised Fuzzy c-Means Clustering Algorithms

  • Yuchi Kanzawa
  • Yasunori Endo
  • Sadaaki Miyamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5861)


In this paper, some semi-supervised clustering methods are proposed with two types of pair constraints: two data have to be together in the same cluster, and two data have to be in different clusters, which are classified into two types: one is based on the standard fuzzy c-means algorithm and the other is on the entropy regularized one. First, the standard fuzzy c-means and the entropy regularized one are introduced. Second, a pairwise constrained semi-supervised fuzzy c means are introduced, which is derived from pairwise constrained competitive agglomeration. Third, some new optimization problem are proposed, which are derived from adding new loss function of memberships to the original optimization problem, respectively. Last, an iterative algorithm is proposed by solving the optimization problem.


Pairwise Constraints Semi-Supervised Clustering Fuzzy c-Means 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bezdek, J.P.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)zbMATHGoogle Scholar
  2. 2.
    Miyamoto, S., Umayahara, K.: Methods in Hard and Fuzzy Clustering. In: Liu, Z.-Q., Miyamoto, S. (eds.) Soft computing and human-centered machines. Springer, Tokyo (2000)Google Scholar
  3. 3.
    Bouchachia, A., Pedrycz, W.: Data Clustering with Partial Supervision. Data Mining and Knowledge Discovery 12, 47–78 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Yamazaki, M., Miyamoto, S., Lee, I.-J.: Semi-supervised Clustering with Two Types of Additional Functions. In: Proc. 24th Fuzzy System Symposium, 2E2-01 (2009)Google Scholar
  5. 5.
    Yamashiro, M., Endo, Y., Hamasuna, Y., Miyamoto, S.: A Study on Semi-supervised Fuzzy c-Means. In: Proc. 24th Fuzzy System Symposium, 2E3-04 (2009)Google Scholar
  6. 6.
    Kanzawa, Y., Endo, Y., Miyamoto, S.: A Semi-Supervised Entropy Regularized Fuzzy c-Means. In: Proc. 2009 International Symposium on Nonlinear Theory and Its Applications (to appear, 2009)Google Scholar
  7. 7.
    Wagstaff, K., Cardie, C., Rogers, S., Schroedl, S.: Constrained K-means Clustering with Background Knowledge. In: Proc. Eighteenth International Conference on Machine-Learning, pp. 577–584 (2001)Google Scholar
  8. 8.
    Frigui, H., Krishnapuram, R.: Clustering by Competitive Agglomeration. Pattern Recognition 30(7), 1109–1119 (1997)CrossRefGoogle Scholar
  9. 9.
    Grira, N., Crucianu, M., Boujemaa, N.: Semi-supervised Image Database Categorization using Pairwise Constraints. In: Proc. 2005 IEEE International Conference on Image Processing, vol. 3, pp. 1228–1231 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yuchi Kanzawa
    • 1
  • Yasunori Endo
    • 2
  • Sadaaki Miyamoto
    • 2
  1. 1.Shibaura Institute of TechnologyTokyoJapan
  2. 2.University of TsukubaJapan

Personalised recommendations