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Transactions on Computational Intelligence XIII pp 132–151Cite as

A Validity Criterion for Fuzzy Clustering

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Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 8342))

Abstract

This paper describes a validity index for fuzzy clustering: Pattern Distances Ratio (PDR) and a cluster number selection procedure using that index.

As other validity indices, solution presented in this paper may be used when a need for assessing of clustering or fuzzy clustering result adequacy arises. Most common example of such situation is when clustering algorithm that requires certain parameter, for example number of clusters, is selected but we lack a priori knowledge of this parameter and we would use educated guesses in concert with trial and error procedures. Validity index may allow to automate such process whenever it is necessary or convenient. In particular, it might ease incorporation of fuzzy clustering into more complex, intelligent systems.

The validity index presented in this paper might be seen as measuring the goodness of clustering of individual examples. When it is averaged over the clustered set, it bears some resemblance to the validity indices based on notions of compactness and separation. During experiments it was used as a cluster number selection criterion for fuzzy c-means. Those experiments showed that PDR can perform well in this role but a special selection procedure should be followed, instead of usual minimum search. The procedure is also described.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Jagiellonian University, Krakow, Poland

    Stanisław Brodowski

Authors
  1. Stanisław Brodowski
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Ngoc-Thanh Nguyen

  2. Laboratory of Theoretical and Applied Computer Science, University of Lorraine, 57045, Metz Cedex, France

    Hoai An Le-Thi

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Brodowski, S. (2014). A Validity Criterion for Fuzzy Clustering. In: Nguyen, NT., Le-Thi, H.A. (eds) Transactions on Computational Intelligence XIII. Lecture Notes in Computer Science, vol 8342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54455-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-54455-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54454-5

  • Online ISBN: 978-3-642-54455-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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