Jaccard Index

This function calculates the Jaccard index. The Jaccard coefficient or Jaccard index is a measure of the similarity of sets. It is used as a measure of similarity for sets, vectors and for objects in general.

To calculate, enter a series of x /y pairs (vectors). The individual numbers are separated by semicolons or spaces. Then click on the 'Calculate' button.

Formula for the Jaccard Index

\(\displaystyle Index= \frac{|A∩B|}{|A∪B|}=\frac{|A∩B|}{|A|+|B|-|A∩B|}\)

\(\displaystyle Distance= 1-Index\)

Example

Jaccard Index of the sets \(\displaystyle A=\{1,2,3,4,5\}\) and \(\displaystyle B=\{4,5,6,7,8\}\)

\(\displaystyle Index= \frac{|A∩B|}{|A∪B|}=\frac{|\{4,5\}|} {|\{1,2,3,4,5,6,7,8\}|} =\frac{2}{8}=0.25\)