Home Â» How to Calculate Cosine Similarity in R

# How to Calculate Cosine Similarity in R

Cosine Similarity is a measure of the similarity between two vectors of an inner product space.

For two vectors, A and B, the Cosine Similarity is calculated as:

Cosine Similarity = Î£AiBi / (âˆšÎ£Ai2âˆšÎ£Bi2)

This tutorial explains how to calculate the Cosine Similarity between vectors in R using theÂ cosine() function from theÂ lsa library.

### Cosine Similarity Between Two Vectors in R

The following code shows how to calculate the Cosine Similarity between two vectors in R:

library(lsa)

#define vectors
a #calculate Cosine Similarity
cosine(a, b)

[,1]
[1,] 0.965195

The Cosine Similarity between the two vectors turns out to beÂ 0.965195.

### Cosine Similarity of a Matrix in R

The following code shows how to calculate the Cosine Similarity between a matrix of vectors:

library(lsa)

#define matrix
a #calculate Cosine Similarity
cosine(data)

a         b         c
a 1.0000000 0.9651950 0.9812406
b 0.9651950 1.0000000 0.9573478
c 0.9812406 0.9573478 1.0000000

Here is how to interpret the output:

• The Cosine Similarity between vectors aÂ andÂ bÂ isÂ 0.9651950.
• The Cosine Similarity between vectors aÂ andÂ c isÂ 0.9812406.
• The Cosine Similarity between vectors b andÂ c isÂ 0.9573478.

### Notes

1. The cosine()Â function will work with a square matrix of any size.

2. TheÂ cosine()Â function will work on a matrix, butÂ notÂ on a data frame. However, you can easily convert a data frame to a matrix in R by using the as.matrix()Â function.