The Duality of Similarity and Metric Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25530%2F21%3A39918024" target="_blank" >RIV/00216275:25530/21:39918024 - isvavai.cz</a>
Alternative codes found
RIV/60461373:22340/21:43923599
Result on the web
<a href="https://www.mdpi.com/2076-3417/11/4/1910" target="_blank" >https://www.mdpi.com/2076-3417/11/4/1910</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/app11041910" target="_blank" >10.3390/app11041910</a>

Result language
angličtina
Original language name
The Duality of Similarity and Metric Spaces
Original language description
We introduce a new mathematical basis for similarity space. For the first time, we describe the relationship between distance and similarity from set theory. Then, we derive generally valid relations for the conversion between similarity and a metric and vice versa. We present a general solution for the normalization of a given similarity space or metric space. The derived solutions lead to many already used similarity and distance functions, and combine them into a unified theory. The Jaccard coefficient, Tanimoto coefficient, Steinhaus distance, Ruzicka similarity, Gaussian similarity, edit distance and edit similarity satisfy this relationship, which verifies our fundamental theory.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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