The Jaccard similarity index 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 R.

**Example: Jaccard Similarity in R**

Suppose we have the following two sets of data:

a <- c(0, 1, 2, 5, 6, 8, 9)b <- c(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 function jaccard <- function(a, b) { intersection = length(intersect(a, b)) union = length(a) + length(b) - intersection return (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 <- c(0, 1, 2, 3, 4, 5) d <- c(6, 7, 8, 9, 10) jaccard(c, d) [1] 0

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

e <- c(0, 1, 2, 3, 4, 5) f <- c(0, 1, 2, 3, 4, 5) jaccard(e, f) [1] 1

The function also works for sets that contain strings:

g <- c('cat', 'dog', 'hippo', 'monkey') h <- c('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 <- c(0, 1, 2, 5, 6, 8, 9) b <- c(0, 2, 3, 4, 5, 7, 9) #find Jaccard distance between setsaandb1 - jaccard(a, b) [1] 0.6

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