# Jaccard Similarity

## #Set #Distance

Jaccard index is the ratio of the size of the intersect of the set and the size of the union of the set.

$$ J(A, B) = \frac{ \vert A \cap B \vert }{ \vert A \cup B \vert } $$

Jaccard distance $d_J(A,B)$ is defined as

$$ d_J(A,B) = 1 - J(A,B). $$

## Properties

If the two sets are the same, $A=B$, we have $J(A,B)=1$ or $d_J(A,B)=0$. We have maximum similarity.

If the two sets have nothing in common, we have $J(A,B)=0$ or $d_J(A,B)=1$. We have minimum similarity.

## Examples

Word Set: (( sentenceOneWords ))

Word Set: (( sentenceTwoWords ))

Intersect: (( intersectWords ))

Union: (( unionWords ))

Jaccard Index: (( jaccardIndex ))

Jaccard Distance: (( jaccardDistance ))

Published:
by Lei Ma;

## Table of Contents

**References:**

**Current Ref:**

- cards/math/jaccard-similarity.md