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Fifty Years of Fuzzy Logic and its Applications pp 315–335Cite as

Handling Noise and Outliers in Fuzzy Clustering

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

Abstract

Since it is an unsupervised data analysis approach, clustering relies solely on the location of the data points in the data space or, alternatively, on their relative distances or similarities. As a consequence, clustering can suffer from the presence of noisy data points and outliers, which can obscure the structure of the clusters in the data and thus may drive clustering algorithms to yield suboptimal or even misleading results. Fuzzy clustering is no exception in this respect, although it features an aspect of robustness, due to which outliers and generally data points that are atypical for the clusters in the data have a lesser influence on the cluster parameters. Starting from this aspect, we provide in this paper an overview of different approaches with which fuzzy clustering can be made less sensitive to noise and outliers and categorize them according to the component of standard fuzzy clustering they modify.

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Notes

  1. 1.

    Note that this approach is not restricted to fuzzy clustering, but can be applied for any clustering scheme, including classical \(c\)-means clustering.

  2. 2.

    Note that computing the membership degrees remains unchanged, regardless of the distance measure and whether it is squared or not, because for this computation the cluster prototypes are fixed and thus the distances are effectively constants.

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Author information

Authors and Affiliations

  1. European Centre for Soft Computing Edificio de Investigacíon, Campus Mieres, c/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt

  2. Dept. Knowledge Processing and Language Engineering, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Christian Braune & Rudolf Kruse

  3. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, 75005, Paris, France

    Marie-Jeanne Lesot

Authors
  1. Christian Borgelt
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  2. Christian Braune
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  3. Marie-Jeanne Lesot
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  4. Rudolf Kruse
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Correspondence to Christian Borgelt .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

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Borgelt, C., Braune, C., Lesot, MJ., Kruse, R. (2015). Handling Noise and Outliers in Fuzzy Clustering. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_17

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_17

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