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Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy
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...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer US
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8924145/ https://www.ncbi.nlm.nih.gov/pubmed/35309152 http://dx.doi.org/10.1007/s00357-021-09395-4 |
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author | Bavaud, François |
author_facet | Bavaud, François |
author_sort | Bavaud, François |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-8924145 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-89241452022-03-17 Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy Bavaud, François J Classif Article 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. Springer US 2021-09-08 2022 /pmc/articles/PMC8924145/ /pubmed/35309152 http://dx.doi.org/10.1007/s00357-021-09395-4 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Bavaud, François Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title | Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title_full | Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title_fullStr | Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title_full_unstemmed | Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title_short | Similarity-Reduced Diversities: the Effective Entropy and the Reduced Entropy |
title_sort | similarity-reduced diversities: the effective entropy and the reduced entropy |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8924145/ https://www.ncbi.nlm.nih.gov/pubmed/35309152 http://dx.doi.org/10.1007/s00357-021-09395-4 |
work_keys_str_mv | AT bavaudfrancois similarityreduceddiversitiestheeffectiveentropyandthereducedentropy |