Jaccard Distance

The Jaccard coefficient measures the similarity of finite sets, and it’s based on how much two finite sets share the same elements.

$J(A,B)=\frac{|A\cap B|}{|A\cup B|}=\frac{|A\cap B|}{|A|+|B|-|A\cap B|}$

It ranges in the $[0,1]$ interval.

Since we use distance instead of similarity most of the times, it’s better to use the Jaccard distance, that’s defined as:

${\delta }_J(A,B)=1-J(A,B)=\frac{|A\cup B|-|A\cap B|}{|A\cup B|}$