Skip to main content
SpringerLink
Log in

Fuzzy Clustering – Basic Ideas and Overview

  • Chapter
Springer Handbook of Computational Intelligence

Part of the book series: Springer Handbooks ((SHB))

  • 10k Accesses

Abstract

This chapter overviews basic formulations as well as recent studies in fuzzy clustering. A major part is devoted to the discussion of fuzzy c-means and their variations. Recent topics such as kernel-based fuzzy c-means and clustering with semi-supervision are mentioned. Moreover, fuzzy hierarchical clustering is overviewed and fundamental theorem is given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

FCM:

fuzzy c-means algorithm

KM:

Karnik–Mendel

References

  1. R.O. Duda, P.E. Hart: Pattern Classification and Scene Analysis (John Wiley, New York 1973)

    MATH  Google Scholar 

  2. B.S. Everitt: Cluster Analysis, 3rd edn. (Arnold, London 1993)

    MATH  Google Scholar 

  3. A.K. Jain, R.C. Dubes: Algorithms for Clustering Data (Prentice Hall, Englewood Cliffs, NJ 1988)

    MATH  Google Scholar 

  4. L. Kaufman, P.J. Rousseeuw: Finding Groups in Data: An Introduction to Cluster Analysis (Wiley, New York 1990)

    Book  Google Scholar 

  5. J.C. Dunn: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cybern. 3, 32–57 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  6. J.C. Dunn: Well-separated clusters and optimal fuzzy partitions, J. Cybern. 4, 95–104 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. J.C. Bezdek: Fuzzy Mathematics in Pattern Classification, Ph.D. Thesis (Cornell Univ., Ithaca 1973)

    Google Scholar 

  8. J.C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum, New York 1981)

    Book  MATH  Google Scholar 

  9. J.C. Bezdek, J. Keller, R. Krishnapuram, N.R. Pal: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing (Kluwer, Boston 1999)

    Book  MATH  Google Scholar 

  10. L.A. Zadeh: Similarity relations and fuzzy orderings, Inf. Sci. 3, 177–200 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Miyamoto: Fuzzy Sets in Information Retrieval and Cluster Analysis (Kluwer, Dordrecht 1990)

    Book  MATH  Google Scholar 

  12. J.B. MacQueen: Some methods of classification and analysis of multivariate observations, Proc. 5th Berkeley Symp. Math. Stat. Prob. (Univ. of California Press, Berkeley 1967) pp. 281–297

    Google Scholar 

  13. S. Miyamoto, H. Ichihashi, K. Honda: Algorithms for Fuzzy Clustering (Springer, Berlin 2008)

    MATH  Google Scholar 

  14. R.J. Hathaway, J.C. Bezdek: Switching regression models and fuzzy clustering, IEEE Trans. Fuzzy Syst. 1(3), 195–204 (1993)

    Article  Google Scholar 

  15. E.E. Gustafson, W.C. Kessel: Fuzzy clustering with a fuzzy covariance matrix, IEEE CDC (1979) pp. 761–766

    Google Scholar 

  16. F. Höppner, F. Klawonn, R. Kruse, T. Runkler: Fuzzy Cluster Analysis (Wiley, New York 1999)

    MATH  Google Scholar 

  17. R. Krishnapuram, J.M. Keller: A possibilistic approach to clustering, IEEE Trans. Fuzzy Syst. 1, 98–110 (1993)

    Article  Google Scholar 

  18. R.N. Davé, R. Krishnapuram: Robust clustering methods: A unified view, IEEE Trans. Fuzzy Syst. 5, 270–293 (1997)

    Article  Google Scholar 

  19. V.N. Vapnik: Statistical Learning Theory (Wiley, New York 1998)

    MATH  Google Scholar 

  20. V.N. Vapnik: The Nature of Statistical Learning Theory, 2nd edn. (Springer, New York 2000)

    Book  MATH  Google Scholar 

  21. B. Schölkopf, A.J. Smola: Learning with Kernels (MIT Press, Cambridge 2002)

    MATH  Google Scholar 

  22. T. Kohonen: Self-Organizing Maps, 2nd edn. (Springer, Berlin 1997)

    Book  MATH  Google Scholar 

  23. S. Miyamoto, D. Suizu: Fuzzy c-means clustering using kernel functions in support vector machines, J. Adv. Comput. Intell. Intell. Inf. 7(1), 25–30 (2003)

    Google Scholar 

  24. O. Chapelle, B. Schölkopf, A. Zien (Eds.): Semi-Supervised Learning (MIT Press, Cambridge 2006)

    Google Scholar 

  25. X. Zhu, A.B. Goldberg: Introduction to Semi-Supervised Learning (Morgan Claypool, San Rafael 2009)

    MATH  Google Scholar 

  26. A. Bouchachia, W. Pedrycz: A semi-supervised clustering algorithm for data exploration, IFSA 2003, Lect. Notes Artif. Intell. 2715, 328–337 (2003)

    MATH  Google Scholar 

  27. S. Miyamoto: An overview of hierarchical and non-hierarchical algorithms of clustering for semi-supervised classification, LNAI 7647, 1–10 (2012)

    Google Scholar 

  28. R.-P. Li, M. Mukaidono: A maximum entropy approach to fuzzy clustering, Proc. 4th IEEE Int. Conf. Fuzzy Syst. (FUZZ-IEEE/IFES'95) (1995) pp. 2227–2232

    Google Scholar 

  29. S. Miyamoto, M. Mukaidono: Fuzzy c-means as a regularization and maximum entropy approach, Proc. 7th Int. Fuzzy Syst. Assoc. World Congr. IFSA'97), Vol. 2 (1997) pp. 86–92

    Google Scholar 

  30. H. Ichihashi, K. Honda, N. Tani: Gaussian mixture PDF approximation and fuzzy c-means clustering with entropy regularization, Proc. 4th Asian Fuzzy Syst. Symp., Vol. 1 (2000) pp. 217–221

    Google Scholar 

  31. H. Ichihashi, K. Miyagishi, K. Honda: Fuzzy c-means clustering with regularization by K-L information, Proc. 10th IEEE Int. Conf. Fuzzy Syst., Vol. 2 (2001) pp. 924–927

    Google Scholar 

  32. S. Basu, I. Davidson, K.L. Wagstaff: Constrained Clustering (CRC, Boca Raton 2009)

    MATH  Google Scholar 

  33. N. Shental, A. Bar-Hillel, T. Hertz, D. Weinshall: Computing Gaussian mixture models with EM using equivalence constraints, Advances in Neural Information Processing Systems 16, ed. by S. Thrun, L.K. Saul, B. Schölkopf (MIT Press, Cambridge 2004)

    Google Scholar 

  34. N. Wang, X. Li, X. Luo: Semi-supervised kernel-based fuzzy c-means with pairwise constraints, Proc. WCCI 2008 (2008) pp. 1099–1103

    Google Scholar 

  35. S. Miyamoto: Statistical and non-statistical models in clustering: An introduction and recent topics, Analysis and Modelling of Complex Data in Behavioural and Social Sciences, JCS-CLADAG 12, ed. by A. Okada, D. Vicari, G. Ragozini (2012) pp. 3–6

    Google Scholar 

  36. M. Ester, H.-P. Kriegel, J. Sander, X.W. Xu: A density-based algorithm for discovering clusters in large spatial databases with noise, Proc. 2nd Int. Conf. Knowl. Discov. Data Min. (KDD-96) (AAAI Press, Menlo Park 1996)

    Google Scholar 

  37. D. Wishart: Mode analysis: A generalization of nearest neighbour which reduces chaining effects, Numer. Taxn., Proc. Colloq., ed. by A.J. Cole (1968) pp. 283–311

    Google Scholar 

  38. E.H. Ruspini: A new approach to clustering, Inf. Control 15, 22–32 (1969)

    Article  MATH  Google Scholar 

  39. D. Dumitrescu, B. Lazzerini, L.C. Jain: Fuzzy Sets and Their Application to Clustering and Training (CRC Press, Boca Raton 2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Risk Engineering, University of Tsukuba, 1-1-1 Tennodai, 305-8573, Tsukuba, Japan

    Sadaaki Miyamoto

Authors
  1. Sadaaki Miyamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sadaaki Miyamoto .

Editor information

Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Miyamoto, S. (2015). Fuzzy Clustering – Basic Ideas and Overview. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43505-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43504-5

  • Online ISBN: 978-3-662-43505-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation