# Overlap coefficient

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{{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](/source/similarity_measure) that measures the overlap between two finite [set](/source/Set_(mathematics))s. It is related to the [Jaccard index](/source/Jaccard_index) and is defined as the size of the [intersection](/source/intersection_(set_theory)) 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](/source/subset) of ''B'' or the converse, then the overlap coefficient is equal to&nbsp;1.

==See also==
* [Jaccard index](/source/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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