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Scaling Dimension

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Formal Concept Analysis (ICFCA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13934))

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Abstract

Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic definitions are in flux. Our contribution was triggered by the study of concept lattices for tree classifiers and the scaling methods used there. We extend some basic notions, give precise mathematical definitions for them and introduce the concept of scaling dimension. In addition to a detailed discussion of its properties, including an example, we show theoretical bounds related to the order dimension of concept lattices. We also study special subclasses, such as the ordinal and the interordinal scaling dimensions, and show for them first results and examples.

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Notes

  1. 1.

    The word “scaling” refers to measurement theory, not whether algorithms can be applied to large data sets.

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Author information

Authors and Affiliations

  1. TU Dresden, Dresden, Germany

    Bernhard Ganter

  2. Knowledge and Data Engineering Group, University of Kassel, Kassel, Germany

    Tom Hanika & Johannes Hirth

  3. Interdisciplinary Research Center for Information System Design, University of Kassel, Kassel, Germany

    Tom Hanika & Johannes Hirth

Authors
  1. Bernhard Ganter
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  2. Tom Hanika
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  3. Johannes Hirth
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Corresponding author

Correspondence to Johannes Hirth .

Editor information

Editors and Affiliations

  1. Universität Kassel, Kassel, Germany

    Dominik Dürrschnabel

  2. Universidad de Málaga, Málaga, Spain

    Domingo López Rodríguez

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Ganter, B., Hanika, T., Hirth, J. (2023). Scaling Dimension. In: Dürrschnabel, D., López Rodríguez, D. (eds) Formal Concept Analysis. ICFCA 2023. Lecture Notes in Computer Science(), vol 13934. Springer, Cham. https://doi.org/10.1007/978-3-031-35949-1_5

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  • DOI: https://doi.org/10.1007/978-3-031-35949-1_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-35948-4

  • Online ISBN: 978-3-031-35949-1

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