How to Calculate Cosine Similarity in R

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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 = ΣA_iB_i / (√ΣA_i²√ΣB_i²)

This tutorial explains how to calculate the Cosine Similarity between vectors in R using the cosine() function from the 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 be 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 a and b is 0.9651950.
• The Cosine Similarity between vectors a and c is 0.9812406.
• The Cosine Similarity between vectors b and c is 0.9573478.

Notes

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

2. The cosine() function will work on a matrix, but not on a data frame. However, you can easily convert a data frame to a matrix in R by using the as.matrix() function.

3. Refer to this Wikipedia page to learn more details about Cosine Similarity.