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The measures the similarity between two sets of data. It can range from 0 to 1. The higher the number, the more similar the two sets of data.

The Jaccard similarity index is calculated as:

Jaccard Similarity = (number of observations in both sets) / (number in either set)

Or, written in notation form:

J(A, B) = |A∩B| / |A∪B|

This tutorial explains how to calculate Jaccard Similarity for two sets of data in Python.

Example: Jaccard Similarity in Python

Suppose we have the following two sets of data:

import numpy as np

a = [0, 1, 2, 5, 6, 8, 9]
b = [0, 2, 3, 4, 5, 7, 9]

We can define the following function to calculate the Jaccard Similarity between the two sets:

#define Jaccard Similarity functiondef jaccard(list1, list2):
    intersection = len(list(set(list1).intersection(list2)))
    union = (len(list1) + len(list2)) - intersection
    return float(intersection) / union

#find Jaccard Similarity between the two sets 
jaccard(a, b)

0.4

The Jaccard Similarity between the two lists is 0.4.

Note that the function will return 0 if the two sets don’t share any values:

c = [0, 1, 2, 3, 4, 5]
d = [6, 7, 8, 9, 10]

jaccard(c, d)

0.0

And the function will return 1 if the two sets are identical:

e = [0, 1, 2, 3, 4, 5]
f = [0, 1, 2, 3, 4, 5]

jaccard(e, f)

1.0

The function also works for sets that contain strings:

g = ['cat', 'dog', 'hippo', 'monkey']
h = ['monkey', 'rhino', 'ostrich', 'salmon']

jaccard(g, h)

0.142857

You can also use this function to find the Jaccard distance between two sets, which is the dissimilarity between two sets and is calculated as 1 – Jaccard Similarity.

a = [0, 1, 2, 5, 6, 8, 9]
b = [0, 2, 3, 4, 5, 7, 9]

#find Jaccard distance between sets a and b
1 - jaccard(a, b)

0.6

Related: How to Calculate Jaccard Similarity in R

Refer to this Wikipedia page to learn more details about the Jaccard Similarity Index.