# 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 = ΣAiBi / (√ΣAi2√ΣBi2)

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 <- c(23, 34, 44, 45, 42, 27, 33, 34)
b <- c(17, 18, 22, 26, 26, 29, 31, 30)

#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 <- c(23, 34, 44, 45, 42, 27, 33, 34)
b <- c(17, 18, 22, 26, 26, 29, 31, 30)
c <- c(34, 35, 35, 36, 51, 29, 30, 31)

data <- cbind(a, b, c)

#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 and is 0.9651950.
• The Cosine Similarity between vectors 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.