Skip to main content
SpringerLink
Log in

Robust Fuzzy Clustering via Trimming and Constraints

  • Conference paper
  • First Online:
Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

Included in the following conference series:

Abstract

A methodology for robust fuzzy clustering is proposed. This methodology can be widely applied in very different statistical problems given that it is based on probability likelihoods. Robustness is achieved by trimming a fixed proportion of “most outlying” observations which are indeed self-determined by the data set at hand. Constraints on the clusters’ scatters are also needed to get mathematically well-defined problems and to avoid the detection of non-interesting spurious clusters. The main lines for computationally feasible algorithms are provided and some simple guidelines about how to choose tuning parameters are briefly outlined. The proposed methodology is illustrated through two applications. The first one is aimed at heterogeneously clustering under multivariate normal assumptions and the second one might be useful in fuzzy clusterwise linear regression problems.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Banerjee A, Davé RN (2012) Robust clustering. Wires Data Min Knowl 2:29–59

    Google Scholar 

  2. Bezdek JC (1981) Pattern recognition with fuzzy objective function algoritms. Plenum Press, New York

    Book  MATH  Google Scholar 

  3. Davé RN (1991) Characterization and detection of noise in clustering. Pattern Recogn Lett 12:657–664

    Google Scholar 

  4. Davé RN, Krishnapuram R (1997) Robust clustering methods: a unified view. IEEE Trans Fuzzy Syst 5:270–293

    Article  Google Scholar 

  5. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39:1–38

    Google Scholar 

  6. Dotto F, Farcomeni A, García-Escudero LA, Mayo-Iscar A (2016) A fuzzy approach to robust regression clustering. Submitted manuscript

    Google Scholar 

  7. Farcomeni A, Greco L (2015) Robust methods for data reduction. Chapman and Hall/CRC, Boca Raton, Florida

    Book  MATH  Google Scholar 

  8. Fritz H, García-Escudero LA, Mayo-Iscar A (2013) Robust constrained fuzzy clustering. Inf Sci 245:38–52

    Article  MathSciNet  MATH  Google Scholar 

  9. García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2008) A general trimming approach to robust cluster analysis. Ann Stat 36:1324–1345

    Article  MathSciNet  MATH  Google Scholar 

  10. García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2010) A review of robust clustering methods. Adv Data Anal Classif 4:89–109

    Article  MathSciNet  MATH  Google Scholar 

  11. García-Escudero LA, Gordaliza A, San Martín R, Mayo-Iscar A (2010) Robust clusterwise linear regresin through trimming. Comput Stat data Anal 54:3057–3069

    Article  MATH  Google Scholar 

  12. Gath I, Geva AB (1989) Unsupervised optimal fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 11:773–781

    Google Scholar 

  13. Gustafson EE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. Proceedings of the IEEE lnternational conference on fuzzy systems, San Diego, pp 761–766 (1979)

    Google Scholar 

  14. Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1:195–204

    Article  Google Scholar 

  15. Hosmer DW (1974) Maximun likelihood estimates of the parameters of a mixture of two regression lines. Commun Stat Theory Methods 3:995–1006

    MATH  Google Scholar 

  16. Kuo-Lung W, Miin-Shen Y, June-Nan H (2009) Alternative fuzzy switching regression. In: Proceedings of the international multiconference of engineers and computer scientist

    Google Scholar 

  17. Kim J, Krishnapuram R, Davé R (1996) Application of the least trimmed squares technique to prototype-based clustering. Pattern Recogn Lett 17:633–641

    Article  Google Scholar 

  18. Klawonn F (2004) Noise clustering with a fixed fraction of noise. In: Lotfi A, Garibaldi JM (eds) Applications and science in soft computing. Springer, Berlin-Heidelberg, pp 133–138

    Google Scholar 

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

    Article  Google Scholar 

  20. Krishnapuram R, Keller JM (1996) The possibilistic \(C\)-means algorithm: Insights and recommandations. IEEE Trans Fuzzy Syst 4:385–393

    Google Scholar 

  21. Lenstra AK, Lenstra JK, Rinnoy Kan AHG, Wansbeek TJ (1982) Two lines least squares. Ann Discrete Math 16:201–211

    MathSciNet  MATH  Google Scholar 

  22. Łeski J (2003) Towards a robust fuzzy clustering. Fuzzy Set Syst 137:215–233

    Article  MathSciNet  MATH  Google Scholar 

  23. Miyamoto S, Mukaidono M (1997) Fuzzy \(c\)-means as a regularization and maximum entropy approach. In: Proceedings of the 7th international fuzzy systems association world congress (IFSA’97), pp 86–92

    Google Scholar 

  24. Ritter G (2015) Robust cluster analysis and variable selection. Monographs on statistics and applied probability. Chapman & Hall/CRC, Boca Raton, Florida

    Google Scholar 

  25. Rousseeuw PJ, Trauwaert E, Kaufman L (1995) Fuzzy clustering with high contrast. J Comput Appl Math 64:81–90

    Article  MathSciNet  MATH  Google Scholar 

  26. Rousseeuw PJ, Kaufman L, Trauwaert E (1996) Fuzzy clustering using scatter matrices. Comput Stat Data Anal 23:135–151

    Article  MATH  Google Scholar 

  27. Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41:212–223

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  29. Späth H (1982) A fast algorithm for clusterwise regression. Computing 29:175–181

    Article  MATH  Google Scholar 

  30. Trauwaert E, Kaufman L, Rousseeuw PJ (1991) Fuzzy clustering algorithms based on the maximum likelihood principle. Fuzzy Sets Syst 42:213–227

    Article  MATH  Google Scholar 

  31. Wu KL, Yang MS (2002) Alternative \(c\)-means clustering algorithms. Pattern Recogn 35:2267–2278

    Article  MATH  Google Scholar 

  32. Yang MS (1993) On a class of fuzzy classification maximum likelihood procedures. Fuzzy Set Syst 57:365–337

    Google Scholar 

Download references

Acknowledgments

Research partially supported by the Spanish Ministerio de Economía y Competitividad, grant MTM2014-56235-C2-1-P, and by Consejería de Educación de la Junta de Castilla y León, grant VA212U13.

Author information

Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Francesco Dotto & Alessio Farcomeni

  2. University of Valladolid, Valladolid, Spain

    Luis Angel García-Escudero & Agustín Mayo-Iscar

Authors
  1. Francesco Dotto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessio Farcomeni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis Angel García-Escudero
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Agustín Mayo-Iscar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luis Angel García-Escudero .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Cite this paper

Dotto, F., Farcomeni, A., García-Escudero, L.A., Mayo-Iscar, A. (2017). Robust Fuzzy Clustering via Trimming and Constraints. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42972-4_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation