How to Calculate Cosine Similarity in Python?

In this article, we calculate the Cosine Similarity between the two non-zero vectors. A vector is a single dimesingle-dimensional signal NumPy array. Cosine similarity is a measure of similarity, often used to measure document similarity in text analysis. We use the below formula to compute the cosine similarity.

Similarity = (A.B) / (||A||.||B||) 

where A and B are vectors:

• A.B is dot product of A and B: It is computed as sum of element-wise product of A and B.
• ||A|| is L2 norm of A: It is computed as square root of the sum of squares of elements of the vector A.

Example 1:

In the example below we compute the cosine similarity between the two vectors (1-d NumPy arrays).  To define a vector here we can also use the Python Lists.

Python

# import required libraries
import numpy as np
from numpy.linalg import norm

# define two lists or array
A = np.array([2,1,2,3,2,9])
B = np.array([3,4,2,4,5,5])

print("A:", A)
print("B:", B)

# compute cosine similarity
cosine = np.dot(A,B)/(norm(A)*norm(B))
print("Cosine Similarity:", cosine)

Output:

Example 2:

In the below example we compute the cosine similarity between a batch of three vectors (2D NumPy array) and a vector(1-D NumPy array). 

Python

# import required libraries
import numpy as np
from numpy.linalg import norm

# define two lists or array
A = np.array([[2,1,2],[3,2,9], [-1,2,-3]])
B = np.array([3,4,2])
print("A:\n", A)
print("B:\n", B)

# compute cosine similarity
cosine = np.dot(A,B)/(norm(A, axis=1)*norm(B))
print("Cosine Similarity:\n", cosine)

Output:

Notice that A has three vectors and B is a single vector. In the above output, we get three elements in the cosine similarity array. The first element corresponds to the cosine similarity between the first vector (first row) of A and the second vector (B). The second element corresponds to the cosine similarity between the second vector (second row ) of A and the second vector (B). And similarly for the third element.

Example 3:

In the below example we compute the cosine similarity between the two 2-d arrays. Here each array has three vectors. Here to compute the dot product using the m of element-wise product.

Python

# import required libraries
import numpy as np
from numpy.linalg import norm

# define two arrays
A = np.array([[1,2,2],
               [3,2,2],
               [-2,1,-3]])
B = np.array([[4,2,4],
               [2,-2,5],
               [3,4,-4]])

print("A:\n", A)
print("B:\n", B)

# compute cosine similarity
cosine = np.sum(A*B, axis=1)/(norm(A, axis=1)*norm(B, axis=1))

print("Cosine Similarity:\n", cosine)
print("Cosine Similarity:\n", cosine)

Output:

The first element of the cosine similarity array is a similarity between the first rows of A and B. Similarly second element is the cosine similarity between the second rows of A and B. Similarly for the third element.