Jaccard index [SEP] named after
Jaccard index
The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally given the French name "coefficient de communauté" by Paul Jaccard), is a statistic used for gauging the similarity and diversity of sample sets. 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:
(If "A" and "B" are both empty, we define "J"("A","B")
Tversky index
The Tversky index, named after Amos Tversky, is an asymmetric similarity measure on sets that compares a variant to a prototype. The Tversky index can be seen as a generalization of Dice's coefficient and Tanimoto coefficient (aka Jaccard index).
For sets "X" and "Y" the Tversky index is a number between 0 and 1 given by
formula_1,
Here, formula_2 denotes the relative complement of Y in X.
Further, formula_3 are parameters of the Tversky index. Setting formula_4 produces