Solved – the significance of the Jaccard similarity score

Question

I understand how to calculate the jaccard similarity , but never quite understood the logic behind why are we calculating it. How does it show the similarity between two sets? What relation exactly does it show?
Can someone throw some light on this?

Answer 1

The Jaccard index is $J(A, B) = \frac{|A \cap B|}{|A\cup B|}$. The numerator $|A \cap B|$ counts the number of times an item occurs in both $A$ and $B$. The denominator $|A\cup B|$ counts the number of distinct items in total in $A$ and $B$.

Hence $J(A, B)$ is the fraction of items that are shared between the two sets.