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Cosine similarity measures the similarity between two lists of vectors by calculating the cosine angle between them. If you consider the cosine function, it has a value of 1 at 0 degrees and -1 at 180 degrees. This means that for two overlapping vectors, for two completely opposite vectors, the cosine value will be the maximum and minimum.

In this article, we will calculate the cosine similarity between two lists of equal size.

scipyCalculate the cosine similarity between two lists in Python using the module

The function from scipythe module spatial.cosine.distance()calculates distance instead of cosine similarity, but to implement this we can subtract the distance value from 1.

For example,

from scipy import spatial

List1 = [4, 47, 8, 3]
List2 = [3, 52, 12, 16]
result = 1 - spatial.distance.cosine(List1, List2)
print(result)

Output:

0.9720951480078084

NumPyCalculate the cosine similarity between two lists in Python using the module

numpy.dot()The function calculates the dot product of two vectors passed as parameters. numpy.norm()The function returns the vector norm.

We can use these functions and the correct formula to calculate cosine similarity.

For example,

from numpy import dot
from numpy.linalg import norm

List1 = [4, 47, 8, 3]
List2 = [3, 52, 12, 16]
result = dot(List1, List2) / (norm(List1) * norm(List2))
print(result)

Output:

0.9720951480078084

If we have multiple or a set of vectors and a query vector to calculate cosine similarity, we can use the following code.

import numpy as np

List1 = np.array([[4, 45, 8, 4], [2, 23, 6, 4]])

List2 = np.array([2, 54, 13, 15])

similarity_scores = List1.dot(List2) / (
    np.linalg.norm(List1, axis=1) * np.linalg.norm(List2)
)

print(similarity_scores)

Output:

[0.98143311 0.99398975]

sklearnCalculate the cosine similarity between two lists in Python using the module

In sklearnthe module, there is a cosine_similarity()built-in function called to calculate cosine similarity.

Please refer to the code below.

from sklearn.metrics.pairwise import cosine_similarity, cosine_distances

A = np.array([10, 3])
B = np.array([8, 7])
result = cosine_similarity(A.reshape(1, -1), B.reshape(1, -1))
print(result)

Output:

[[0.91005765]]

torchCalculate the cosine similarity between two lists in Python using the module

When we are dealing with an N-dimensional tensor with shape (m,n) , we can use the function torchfrom the module consine_similarity()to find the cosine similarity.

For example,

import torch
import torch.nn.functional as F

t1 = [3, 45, 6, 8]
a = torch.FloatTensor(t1)

t2 = [4, 54, 3, 7]
b = torch.FloatTensor(t2)
result = F.cosine_similarity(a, b, dim=0)

print(result)

Output:

tensor(0.9960)

Use torch.FloatTensor()the module to convert lists into tensors.