Jaccard index [SEP] discoverer or inventor
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")
dummy variables, such as binary gender, would be better compared with the SMC than with the Jaccard index since the impact of gender on similarity should be equal, independently of whether male is defined as a 0 and female as a 1 or the other way around. However, when we have symmetric dummy variables, one could replicate the behaviour of the SMC by splitting the dummies into two binary attributes (in this case, male and female), thus transforming them into asymmetric attributes, allowing the use of the Jaccard index