Skip to main content
SpringerLink
Log in

Generalized Fuzzy c-Means Clustering and Its Theoretical Properties

  • Conference paper
  • First Online:
Modeling Decisions for Artificial Intelligence (MDAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11144))

Abstract

This study shows that a generalized fuzzy c-means (gFCM) clustering algorithm, which covers standard fuzzy c-means clustering, can be constructed if a given fuzzified function, its derivative, and its inverse derivative can be calculated. Furthermore, our results show that the fuzzy classification function for gFCM exhibits similar behavior to that of standard fuzzy c-means clustering.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. MacQueen, J.B.: Some methods of classification and analysis of multivariate observations. In: Proceedings the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)

    Google Scholar 

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

    Book  Google Scholar 

  3. 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). https://doi.org/10.1007/978-4-431-67907-3_5

    Chapter  MATH  Google Scholar 

  4. Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78737-2

    Book  MATH  Google Scholar 

  5. Miyamoto, S., Kurosawa, N.: Controlling cluster volume sizes in fuzzy \(c\)-means Clustering. In: Proceedings of SCIS & ISIS 2004, pp. 1–4 (2004)

    Google Scholar 

  6. Ichihashi, H., Honda, K., Tani, N.: Gaussian mixture PDF approximation and fuzzy \(c\)-means clustering with entropy regularization. In: Proceedings of the 4th Asian Fuzzy System Symposium, pp. 217–221 (2000)

    Google Scholar 

  7. Dhillon, I.S., Modha, D.S.: Concept decompositions for large sparse text data using clustering. Mach. Learn. 42, 143–175 (2001)

    Article  Google Scholar 

  8. Miyamoto, S., Mizutani, K.: Fuzzy multiset model and methods of nonlinear document clustering for information retrieval. In: Torra, V., Narukawa, Y. (eds.) MDAI 2004. LNCS (LNAI), vol. 3131, pp. 273–283. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27774-3_26

    Chapter  MATH  Google Scholar 

  9. Mizutani, K., Inokuchi, R., Miyamoto, S.: Algorithms of nonlinear document clustering based on fuzzy set model. Int. J. Intell. Syst. 23(2), 176–198 (2008)

    Article  Google Scholar 

  10. Kanzawa, Y.: On kernelization for a maximizing model of Bezdek-like spherical fuzzy c-means clustering. In: Torra, V., Narukawa, Y., Endo, Y. (eds.) MDAI 2014. LNCS (LNAI), vol. 8825, pp. 108–121. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12054-6_10

    Chapter  Google Scholar 

  11. Kanzawa, Y.: A maximizing model of bezdek-like spherical fuzzy \(c\)-means. J. Adv. Comput. Intell. Intell. Inform. 19(5), 662–669 (2015)

    Article  Google Scholar 

  12. Kanzawa, Y.: A maximizing model of spherical Bezdek-type fuzzy multi-medoids clustering. J. Adv. Comput. Intell. Intell. Inform. 19(6), 738–746 (2015)

    Article  Google Scholar 

  13. Oh, C., Honda, K., Ichihashi, H.: Fuzzy clustering for categorical multivariate data. In: Proceedings IFSA World Congress and 20th NAFIPS International Conference, pp. 2154–2159 (2001)

    Google Scholar 

  14. Honda, K., Oshio, S., Notsu, A.: FCM-type fuzzy co-clustering by K-L information regularization. In: Proceedings of 2014 IEEE International Conference on Fuzzy Systems, pp. 2505–2510 (2014)

    Google Scholar 

  15. Honda, K., Oshio, S., Notsu, A.: Item membership fuzzification in fuzzy co-clustering based on multinomial mixture concept. In: Proceedings of 2014 IEEE International Conference on Granular Computing, pp. 94–99 (2014)

    Google Scholar 

  16. Kanzawa, Y.: Fuzzy co-clustering algorithms based on fuzzy relational clustering and TIBA imputation. J. Adv. Comput. Intell. Intell. Inform. 18(2), 182–189 (2014)

    Article  Google Scholar 

  17. Kanzawa, Y.: On possibilistic clustering methods based on Shannon/Tsallis-entropy for spherical data and categorical multivariate data. In: Torra, V., Narukawa, Y. (eds.) MDAI 2015. LNCS (LNAI), vol. 9321, pp. 115–128. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23240-9_10

    Chapter  Google Scholar 

  18. Kanzawa, Y.: Bezdek-type fuzzified co-clustering algorithm. J. Adv. Comput. Intell. Intell. Inform. 19(6), 852–860 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shibaura Institute of Technology, Tokyo, Japan

    Yuchi Kanzawa

  2. University of Tsukuba, Tsukuba, Japan

    Sadaaki Miyamoto

Authors
  1. Yuchi Kanzawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sadaaki Miyamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuchi Kanzawa .

Editor information

Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Department Management Science, Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

  3. University of the Balearic Islands, Palma de Mallorca, Spain

    Isabel Aguiló

  4. University of the Balearic Islands, Palma de Mallorca, Baleares, Spain

    Manuel González-Hidalgo

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kanzawa, Y., Miyamoto, S. (2018). Generalized Fuzzy c-Means Clustering and Its Theoretical Properties. In: Torra, V., Narukawa, Y., Aguiló, I., González-Hidalgo, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2018. Lecture Notes in Computer Science(), vol 11144. Springer, Cham. https://doi.org/10.1007/978-3-030-00202-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00202-2_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00201-5

  • Online ISBN: 978-3-030-00202-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation