Skip to main content

Developing Additive Spectral Approach to Fuzzy Clustering

  • Conference paper
  • 1117 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6743))

Abstract

An additive spectral method for fuzzy clustering is presented. The method operates on a clustering model which is an extension of the spectral decomposition of a square matrix. The computation proceeds by extracting clusters one by one, which allows us to draw several stopping rules to the procedure. We experimentally test the performance of our method and show its competitiveness.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bezdek, J., Keller, J., Krishnapuram, R., Pal, T.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers, Dordrecht (1999)

    Book  MATH  Google Scholar 

  2. Brouwer, R.: A method of relational fuzzy clustering based on producing feature vectors using FastMap. Information Sciences 179, 3561–3582 (2009)

    Article  Google Scholar 

  3. Davé, R., Sen, S.: Robust fuzzy clustering of relational data. IEEE Transactions on Fuzzy Systems 10, 713–727 (2002)

    Article  Google Scholar 

  4. Hathaway, R.J., Bezdek, J.C.: NERF c-means: Non-Euclidean relational fuzzy clustering. Pattern Recognition 27, 429–437 (1994)

    Article  Google Scholar 

  5. Hubert, L.J., Arabie, P.: Comparing partitions. Journal of Classification 2, 193–218 (1985)

    Article  MATH  Google Scholar 

  6. von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17, 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  7. Mirkin, B.: Additive clustering and qualitative factor analysis methods for similarity matrices. Journal of Classification 4(1), 7–31 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mirkin, B., Nascimento, S.: Analysis of Community Structure, Affinity Data and Research Activities using Additive Fuzzy Spectral Clustering. Technical Report 6, School of Computer Science, Birkbeck University of London (2009)

    Google Scholar 

  9. Roubens, M.: Pattern classification problems and fuzzy sets. Fuzzy Sets and Systems 1, 239–253 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sato, M., Sato, Y., Jain, L.C.: Fuzzy Clustering Models and Applications. Physica-Verlag, Heidelberg (1997)

    MATH  Google Scholar 

  11. Shepard, R.N., Arabie, P.: Additive clustering: representation of similarities as combinations of overlapping properties. Psychological Review 86, 87–123 (1979)

    Article  Google Scholar 

  12. Windham, M.P.: Numerical classification of proximity data with assignment measures. Journal of Classification 2, 157–172 (1985)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mirkin, B.G., Nascimento, S. (2011). Developing Additive Spectral Approach to Fuzzy Clustering. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21881-1_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21880-4

  • Online ISBN: 978-3-642-21881-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics