[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

Alternative Fuzzy Clustering Algorithms with L1-Norm and Covariance Matrix

  • Conference paper
Advanced Concepts for Intelligent Vision Systems (ACIVS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4179))

Abstract

In fuzzy clustering, the fuzzy c-means (FCM) algorithm is the best known and most used method. Although FCM is a very useful method, it is sensitive to noise and outliers so that Wu and Yang (2002) proposed an alternative FCM (AFCM) algorithm. In this paper, we consider the AFCM algorithms with L1-norm and fuzzy covariance. These generalized AFCM algorithms can detect elliptical shapes of clusters and also robust to noise and outliers. Some numerical experiments are performed to assess the performance of the proposed algorithms. Numerical results clearly indicate the proposed algorithms to be superior to the existing methods.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Bobrowski, L., Bezdek, J.C.: C-Means Clustering with the L1 and L ∞  Norms. IEEE Trans. Systems, Man, and Cybernetics 21, 545–554 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gustafson, D.E., Kessel, W.C.: Fuzzy Clustering with a Fuzzy Covariance Matrix. In: IEEE CDC, San Diego, CA, pp. 10–12 (1979)

    Google Scholar 

  4. Hathaway, R.J., Bezdek, J.C., Hu, Y.: Generalized Fuzzy C-Means Clustering Strategies Using Lp Norm Distances. IEEE Trans. Fuzzy Systems 8, 576–582 (2000)

    Article  Google Scholar 

  5. Hoppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification Data Analysis and Image Recognition. Wiley, New York (1999)

    Google Scholar 

  6. Jajuga, K.: L1-norm based fuzzy clustering. Fuzzy set and Systems 39, 43–50 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kersten, P.R.: Fuzzy Order Statistics and Their Application to Fuzzy Clustering. IEEE Trans. Fuzzy Systems 7, 708–712 (1999)

    Article  Google Scholar 

  8. Krishnapuram, R., Kim, J.: A Note on the Gustafson-Kessel and Adaptive Fuzzy Clustering Algorithms. IEEE Trans. Fuzzy Systems 7, 453–461 (1999)

    Article  Google Scholar 

  9. Wu, K.L., Yang, M.S.: Alternative C-Means Clustering Algorithms. Pattern Recognition 35, 2267–2278 (2002)

    Article  MATH  Google Scholar 

  10. Yang, M.S.: A Survey of Fuzzy Clustering. Mathematical and Computer Modeling 18, 1–16 (1993)

    Article  MATH  Google Scholar 

  11. Yu, J., Yang, M.S.: Optimality Test for Generalized FCM and Its Application to Parameter Selection. IEEE Trans. Fuzzy Systems 13, 164–176 (2005)

    Article  Google Scholar 

  12. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan

    Miin-Shen Yang & Tsiung-Iou Chung

  2. Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan

    Wen-Liang Hung

Authors
  1. Miin-Shen Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-Liang Hung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tsiung-Iou Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. DGA/D4S/MRIS, 94114, Arcueil, France

    Jacques Blanc-Talon

  2. Ghent University, 9000, Gent, Belgium

    Wilfried Philips

  3. CSIRO ICT Centre, 1710, Sydney, NSW, Australia

    Dan Popescu

  4. University of Antwerp, 2610, Wilrijk, Belgium

    Paul Scheunders

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yang, MS., Hung, WL., Chung, TI. (2006). Alternative Fuzzy Clustering Algorithms with L1-Norm and Covariance Matrix. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2006. Lecture Notes in Computer Science, vol 4179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864349_60

Download citation

  • DOI: https://doi.org/10.1007/11864349_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44630-9

  • Online ISBN: 978-3-540-44632-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation