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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 numpy as np
from numpy.linalg import norm
A = np.array[[2,1,2,3,2,9]]
B =
np.array[[3,4,2,4,5,5]]
print["A:", A]
print["B:", B]
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 numpy as np
from numpy.linalg import norm
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]
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 numpy as np
from numpy.linalg import norm
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]
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.