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Fuzzy Clustering

  • Chapter
Computational Intelligence

Part of the book series: Texts in Computer Science ((TCS))

Abstract

After a brief overview of fuzzy methods in data analysis, this chapter focuses on fuzzy cluster analysis as the oldest fuzzy approach to data analysis. Fuzzy clustering comprises a family of prototype-based clustering methods that can be formulated as the problem of minimizing an objective function. These methods can be seen as “fuzzifications” of, for example, the classical c-means algorithm, which strives to minimize the sum of the (squared) distances between the data points and the cluster centers to which they are assigned. However, in order to “fuzzify” such a crisp clustering approach, it is not enough to merely allow values from the unit interval for the variables encoding the assignments of the data points to the clusters: the minimum is still obtained for a crisp data point assignment. As a consequence, additional means have to be employed in the objective function in order to obtain actual degrees of membership. This chapter surveys the most common fuzzification means and examines and compares their properties.

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Authors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University Magdeburg, Magdeburg, Germany

    Rudolf Kruse, Christian Moewes & Pascal Held

  2. Intelligent Data Analysis & Graphical Models Research Unit, European Centre for Soft Computing, Mieres, Spain

    Christian Borgelt

  3. FB Informatik, Ostfalia University of Applied Sciences, Wolfenbüttel, Germany

    Frank Klawonn

  4. SAP Innovation Center, Potsdam, Germany

    Matthias Steinbrecher

Authors
  1. Rudolf Kruse
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  2. Christian Borgelt
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  3. Frank Klawonn
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  4. Christian Moewes
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  5. Matthias Steinbrecher
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  6. Pascal Held
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Kruse, R., Borgelt, C., Klawonn, F., Moewes, C., Steinbrecher, M., Held, P. (2013). Fuzzy Clustering. In: Computational Intelligence. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-5013-8_20

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  • DOI: https://doi.org/10.1007/978-1-4471-5013-8_20

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  • Online ISBN: 978-1-4471-5013-8

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