{{Short description|Similarity measure between sets}} The '''overlap coefficient''',{{refn|group=note|The use of the term "overlap" appears in the comment for formula #27 in Table 2 of McGill ''et al''. (1979),<ref name="McGill1979"/> which references Sager & Lockemann (1976).<ref name="SagerLockemann"/>}} or '''Szymkiewicz–Simpson coefficient''',{{Citation needed|reason=need Szymkiewicz citation|date=May 2024}}<ref name="Simpson1943"/><ref name="Simpson1947"/><ref name="Simpson1960"/> is a similarity measure that measures the overlap between two finite sets. It is related to the Jaccard index and is defined as the size of the intersection divided by the size of the smaller of two sets:

:<math>\operatorname{overlap}(A,B) = \frac{| A \cap B | }{\min(|A|,|B|)}</math>

Note that <math>0 \leq \operatorname{overlap}(A,B) \leq 1</math>. If set ''A'' is a subset of ''B'' or the converse, then the overlap coefficient is equal to&nbsp;1.

==See also== * Jaccard index

==Notes== {{reflist|group=note}}

==References== <references>

<ref name="SagerLockemann">Sager, W. K. H.; Lockemann, P. C. (1976). "Classification of Ranking Algorithms". ''International Forum on Information and Documentation''. '''1''' (4): 12–25.</ref> <ref name="McGill1979">McGill, M.; Koll, M.; Noreault, T. (October 1979). [https://files.eric.ed.gov/fulltext/ED188587.pdf ''An Evaluation of Factors Affecting Document Ranking by Information Retrieval Systems''], Syracuse, NY: School of Information Studies, Syracuse University.</ref> <ref name="Simpson1943">Simpson, G. G. (January 1943). [https://people.wku.edu/charles.smith/biogeog/SIMP943A.htm "Mammals and the Nature of Continents"]. ''American Journal of Science''. '''241''' (1): 1–31.</ref> <ref name="Simpson1947">Simpson, G. G. (July 1947). "Holarctic Mammalian Faunas and the Continental Relationships During the Cenozoic". ''Bulletin of the Geological Society of America''. '''58''' (7): 613–688.</ref> <ref name="Simpson1960">Simpson, G. G. (1960). [https://biocomparison.ucoz.ru/_ld/0/42_Simpson_1960.pdf "Notes on the Measurement of Faunal Resemblance"]. ''American Journal of Science''. '''258-A''': 300–311.</ref>

</references>

Category:Information retrieval techniques Category:Information retrieval evaluation Category:Measure theory Category:Similarity measures

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