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Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy

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  • François Bavaud

    (Institute of Geography and Sustainability University of Lausanne)

Abstract

The paper presents and analyzes the properties of a new diversity index, the effective entropy, which lowers Shannon entropy by taking into account the presence of similarities between items. Similarities decrease exponentially with the item dissimilarities, with a freely adjustable discriminability parameter controlling various diversity regimes separated by phase transitions. Effective entropies are determined iteratively, and turn out to be concave and subadditive, in contrast to the reduced entropy, proposed in Ecology for similar purposes. Two data sets are used to illustrate the formalism, and underline the role played by the dissimilarity types.

Suggested Citation

  • François Bavaud, 2022. "Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 100-121, March.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:1:d:10.1007_s00357-021-09395-4
    DOI: 10.1007/s00357-021-09395-4
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    References listed on IDEAS

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    1. François Bavaud, 2011. "On the Schoenberg Transformations in Data Analysis: Theory and Illustrations," Journal of Classification, Springer;The Classification Society, vol. 28(3), pages 297-314, October.
    2. François Bavaud, 2009. "Aggregation invariance in general clustering approaches," 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 205-225, December.
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