The cosine similarity between two vectors is calculated by taking the dot product of the vectors and dividing it by the product of the magnitudes of the vectors.

Step 1: Calculate the dot product of w1 and w2.
Dot product = (0.2*0.3) + (0.1*0) + (0.3*0.2) + (0.4*0.5) = 0.06 + 0 + 0.06 + 0.2 = 0.32

Step 2: Calculate the magnitude of w1.
Magnitude of w1 = sqrt((0.2)^2 + (0.1)^2 + (0.3)^2 + (0.4)^2) = sqrt(0.04 + 0.01 + 0.09 + 0.16) = sqrt(0.3)

Step 3: Calculate the magnitude of w2.
Magnitude of w2 = sqrt((0.3)^2 + (0)^2 + (0.2)^2 + (0.5)^2) = sqrt(0.09 + 0 + 0.04 + 0.25) = sqrt(0.38)

Step 4: Divide the dot product by the product of the magnitudes.
Cosine similarity = 0.32 / (sqrt(0.3) * sqrt(0.38)) = 0.32 / (0.5477 * 0.6164) = 0.32 / 0.3375 = 0.948

So, the cosine similarity between w1 and w2 is 0.948. Therefore, the answer is a. 0.948.

Question

The cosine similarity between two vectors is calculated by taking the dot product of the vectors and dividing it by the product of the magnitudes of the vectors.

Step 1: Calculate the dot product of w1 and w2.
Dot product = (0.2*0.3) + (0.1*0) + (0.3*0.2) + (0.4*0.5) = 0.06 + 0 + 0.06 + 0.2 = 0.32

Step 2: Calculate the magnitude of w1.
Magnitude of w1 = sqrt((0.2)^2 + (0.1)^2 + (0.3)^2 + (0.4)^2) = sqrt(0.04 + 0.01 + 0.09 + 0.16) = sqrt(0.3)

Step 3: Calculate the magnitude of w2.
Magnitude of w2 = sqrt((0.3)^2 + (0)^2 + (0.2)^2 + (0.5)^2) = sqrt(0.09 + 0 + 0.04 + 0.25) = sqrt(0.38)

Step 4: Divide the dot product by the product of the magnitudes.
Cosine similarity = 0.32 / (sqrt(0.3) * sqrt(0.38)) = 0.32 / (0.5477 * 0.6164) = 0.32 / 0.3375 = 0.948

So, the cosine similarity between w1 and w2 is 0.948. Therefore, the answer is a. 0.948.

Knowee AI · Accepted Answer

The cosine similarity between two vectors is calculated by taking the dot product of the vectors and dividing it by the product of the magnitudes of the vectors.

Step 1: Calculate the dot product of w1 and w2.
Dot product = (0.2*0.3) + (0.1*0) + (0.3*0.2) + (0.4*0.5) = 0.06 + 0 + 0.06 + 0.2 = 0.32

Step 2: Calculate the magnitude of w1.
Magnitude of w1 = sqrt((0.2)^2 + (0.1)^2 + (0.3)^2 + (0.4)^2) = sqrt(0.04 + 0.01 + 0.09 + 0.16) = sqrt(0.3)

Step 3: Calculate the magnitude of w2.
Magnitude of w2 = sqrt((0.3)^2 + (0)^2 + (0.2)^2 + (0.5)^2) = sqrt(0.09 + 0 + 0.04 + 0.25) = sqrt(0.38)

Step 4: Divide the dot product by the product of the magnitudes.
Cosine similarity = 0.32 / (sqrt(0.3) * sqrt(0.38)) = 0.32 / (0.5477 * 0.6164) = 0.32 / 0.3375 = 0.948

So, the cosine similarity between w1 and w2 is 0.948. Therefore, the answer is a. 0.948.

Let us suppose that you have the following two 4-dimensional word vectors for two words, w1 and w2, respectively: w1 =(0.2, 0.1, 0.3, 0.4) and w2 = (0.3, 0, 0.2, 0.5) What is the cosine similarity between w1 and w2?Question 6Answera.0.948b.0c. 0.832d.0.5

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