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

François Bavaud ()
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François Bavaud: Institute of Geography and Sustainability University of Lausanne

Journal of Classification, 2022, vol. 39, issue 1, No 7, 100-121

Abstract: 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.

Keywords: Similarity-reduced diversity; Confusion matrix; Rate distortion function; Phase transitions; Rao quadratic entropy (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00357-021-09395-4

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