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The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used for gauging the similarity and diversity of sample sets. It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v)[1] and now is frequently referred to as the Critical Success Index in meteorology.[2] It was later developed independently by Paul Jaccard, originally giving the French name coefficient de communauté,[3] and independently formulated again by T. Tanimoto.[4] Thus, the Tanimoto index or Tanimoto coefficient are also used in some fields. However, they are identical in generally taking the ratio of Intersection over Union. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:

Note that by design, 0 ≤ J ( A , B ) ≤ 1. {\displaystyle 0\leq J(A,B)\leq 1.} If A intersection B is empty, then J(A,B) = 0. The Jaccard coefficient is widely used in computer science, ecology, genomics, and other sciences, where binary or binarized data are used. Both the exact solution and approximation methods are available for hypothesis testing with the Jaccard coefficient.[5]

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