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 librariesimport numpy as npfrom numpy.linalg import norm# define two lists or arrayA = 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 similaritycosine = 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 librariesimport numpy as npfrom numpy.linalg import norm# define two lists or arrayA = 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 similaritycosine = 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 librariesimport numpy as npfrom numpy.linalg import norm# define two arraysA = 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 similaritycosine = 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.
