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Prototype Based Fuzzy Clustering Algorithms in High-Dimensional Feature Spaces

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Enric Trillas: A Passion for Fuzzy Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 322))

Abstract

The ‘Curse of Dimensionality’ is formulated in a mathematical way that is useful to understand the problems of clustering in high-dimensional spaces. Clustering tasks in high-dimensional spaces have a set of very difficult challenges, especially for one of the most widely used clustering algorithms: Fuzzy c-Means. Three alternatives to Fuzzy c-Means are described that can overcome its problems.

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References

  1. Bellman, R.E.: Dynamic Programming. Dover Books on Mathematics. Dover Publications, Princeton (2003)

    MATH  Google Scholar 

  2. Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U.: When is nearest neighbor meaningful? In: Database Theory—ICDT’99. Lecture Notes in Computer Science, vol. 1540, pp. 217–235. Springer, Berlin (1999)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  4. Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Cybern. Syst.: Int. J. 3(3), 32–57 (1973)

    MATH  MathSciNet  Google Scholar 

  5. Höppner, F., Klawonn, F.: A new approach to fuzzy partitioning. In: Proceedings of the Joint 9th IFSA World Congress and 20th NAFIPS International Conference, pp. 1419–1424 (2001)

    Google Scholar 

  6. Höppner, F., Klawonn, F.: Improved fuzzy partitions for fuzzy regression models. Int. J. Approx. Reason. 32(2–3), 85–102 (2003)

    Article  MATH  Google Scholar 

  7. Klawonn, F., Höppner, F.: What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier. In: Berthold, M.R., Lenz, H.-J., Bradley, E., Kruse, R., Borgelt, C. (eds.) Advances in Intelligent Data Analysis V. Lecture Notes in Computer Science, vol. 2810, pp. 254–264. Springer, Berlin (2003)

    Chapter  Google Scholar 

  8. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)

    Google Scholar 

  9. Winkler, R., Klawonn, F., Kruse, R.: Fuzzy c-means in high dimensional spaces. IJFSA 1(1), 1–16 (2011)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Leibniz-Institution for Astrophysics Potsdam, An der Sternwarte 16, 14482, Potsdam, Germany

    Roland Winkler

  2. Ostfalia University of Applied Sciences, Salzdahlumer Str. 46/48, 38302, Wolfenbuettel, Germany

    Frank Klawonn

  3. Helmholtz Centre for Infection Research, Inhoffenstr. 7, 38124, Braunschweig, Germany

    Frank Klawonn

  4. Otto-von-Guericke-Universitt Magdeburg, Universittsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

Authors
  1. Roland Winkler
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  2. Frank Klawonn
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  3. Rudolf Kruse
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Corresponding author

Correspondence to Roland Winkler .

Editor information

Editors and Affiliations

  1. European Centre for Soft Computing, Asturias, Spain

    Luis Magdalena

  2. Depto. de Ciencias de la Computación e Inteligencia Artificial, University of Granada, Granada, Spain

    Jose Luis Verdegay

  3. Spanish Council for Scientific Research (CSIC), Artificial Intelligence Research Institute (IIIA-CSIC), Catalonia, Spain

    Francesc Esteva

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Winkler, R., Klawonn, F., Kruse, R. (2015). Prototype Based Fuzzy Clustering Algorithms in High-Dimensional Feature Spaces. In: Magdalena, L., Verdegay, J., Esteva, F. (eds) Enric Trillas: A Passion for Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-16235-5_18

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  • DOI: https://doi.org/10.1007/978-3-319-16235-5_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16234-8

  • Online ISBN: 978-3-319-16235-5

  • eBook Packages: EngineeringEngineering (R0)

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