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Totally Balanced Dissimilarities

Author

Listed:
  • François Brucker

    (LIf, CNRS UMR 7279)

  • Pascal Préa

    (LIf, CNRS UMR 7279)

  • Célia Châtel

    (LIf, CNRS UMR 7279)

Abstract

We show in this paper a bijection between totally balanced hypergraphs and so-called totally balanced dissimilarities. We give an efficient way (O(n3) where n is the number of elements) to (i) recognize if a given dissimilarity is totally balanced and (ii) approximate it if it is not the case. We also introduce a new kind of dissimilarity which generalizes chordal graphs and allows a polynomial number of clusters that can be easily computed and interpreted.

Suggested Citation

  • François Brucker & Pascal Préa & Célia Châtel, 2020. "Totally Balanced Dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 203-222, April.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:1:d:10.1007_s00357-019-09320-w
    DOI: 10.1007/s00357-019-09320-w
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    References listed on IDEAS

    as
    1. Fuad Aleskerov & Boris Goldengorin & Panos M. Pardalos (ed.), 2014. "Clusters, Orders, and Trees: Methods and Applications," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4939-0742-7, September.
    2. François Brucker & Alain Gély, 2009. "Parsimonious cluster systems," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 3(3), pages 189-204, December.
    3. Patrice Bertrand & Jean Diatta, 2014. "Weak Hierarchies: A Central Clustering Structure," Springer Optimization and Its Applications, in: Fuad Aleskerov & Boris Goldengorin & Panos M. Pardalos (ed.), Clusters, Orders, and Trees: Methods and Applications, edition 127, pages 211-230, Springer.
    Full references (including those not matched with items on IDEAS)

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