The Jaccard index, popularly known as the Jaccard similarity coefficient is a static used for comparing the similarity and diversity of sample sets. The Jaccard coefficient which measures similarity between sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:
J (A, B) = |A Ώ B|
| A U B|
The Jaccard distance, which measures dissimilarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:
J’ (A,B)=1- J(A.B) = | A U B|-|A Ώ B|
| A U B|
Jaccard’s coefficient (measure similarity) and Jaccard’s distance (measure dissimilarity) are measurement of asymmetric information on binary and non binary variables.