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On Ziggurats and Dendrograms

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Abstract

The indeterminacy in the horizontal ordering of the objects in the usual tree diagram representation of a dendrogram, and the associated dangers of misinterpretation, are well-known. A systematic choice of ordering is presented and seen to have a variety of attractive features. In particular, it induces a strengthened form of the Robinson property of the associated ultrametric matrix, permitting an exact one dimensional visual display of maximal subsets of objects. These systematic orderings are based upon the ziggurat decomposition of an arbitrary binary dendrogram. Worked examples motivate and illustrate the development. Connections with ‘chaining’ in single-link hierarchical cluster analysis are noted.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK

    Frank Critchley

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  1. Frank Critchley
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Editor information

Editors and Affiliations

  1. Department of Information Systems, University of Mannheim, Schloss, 68131, Mannheim, Germany

    Martin Schader

  2. Institute of Decision Theory, University of Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany

    Wolfgang Gaul

  3. Department of Statistics, University of Rome, Piazzale Aldo Moro, 00185, Rome, Italy

    Maurizio Vichi

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© 2003 Springer-Verlag Berlin Heidelberg

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Critchley, F. (2003). On Ziggurats and Dendrograms. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_22

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  • DOI: https://doi.org/10.1007/978-3-642-18991-3_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40354-8

  • Online ISBN: 978-3-642-18991-3

  • eBook Packages: Springer Book Archive

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