To find the cosine similarity between two documents, we first need to convert the text into vectors. This can be done using a method called Bag of Words or TF-IDF. Here, we'll use Bag of Words for simplicity.

Step 1: Create a list of unique words from both documents.
Unique words: 'the', 'best', 'data', 'science', 'course', 'is', 'popular'

Step 2: Create vectors for both documents. The vectors will have as many dimensions as there are unique words. Each dimension will contain the count of the times each word appears in the document.

Vector for Document 1: [1, 1, 1, 1, 1, 0, 0] (the word 'the' appears once, 'best' appears once, 'data' appears once, 'science' appears once, 'course' appears once, 'is' does not appear, 'popular' does not appear)

Vector for Document 2: [0, 0, 1, 1, 0, 1, 1] (the word 'the' does not appear, 'best' does not appear, 'data' appears once, 'science' appears once, 'course' does not appear, 'is' appears once, 'popular' appears once)

Step 3: Calculate the cosine similarity. The cosine similarity is the dot product of the two vectors divided by the product of the magnitudes of both vectors.

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

A.B = (1*0 + 1*0 + 1*1 + 1*1 + 1*0 + 0*1 + 0*1) = 2

||A|| = sqrt(1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 0^2 + 0^2) = sqrt(5)

||B|| = sqrt(0^2 + 0^2 + 1^2 + 1^2 + 0^2 + 1^2 + 1^2) = sqrt(4)

Cosine Similarity = 2 / (sqrt(5) * sqrt(4)) = 2 / (2.236067977 * 2) = 0.447213595

So, the cosine similarity of the two documents is approximately 0.447, which is closest to option 1. Therefore, the answer is 1. 0.44721.

Question

To find the cosine similarity between two documents, we first need to convert the text into vectors. This can be done using a method called Bag of Words or TF-IDF. Here, we'll use Bag of Words for simplicity.

Step 1: Create a list of unique words from both documents.
Unique words: 'the', 'best', 'data', 'science', 'course', 'is', 'popular'

Step 2: Create vectors for both documents. The vectors will have as many dimensions as there are unique words. Each dimension will contain the count of the times each word appears in the document.

Vector for Document 1: [1, 1, 1, 1, 1, 0, 0] (the word 'the' appears once, 'best' appears once, 'data' appears once, 'science' appears once, 'course' appears once, 'is' does not appear, 'popular' does not appear)

Vector for Document 2: [0, 0, 1, 1, 0, 1, 1] (the word 'the' does not appear, 'best' does not appear, 'data' appears once, 'science' appears once, 'course' does not appear, 'is' appears once, 'popular' appears once)

Step 3: Calculate the cosine similarity. The cosine similarity is the dot product of the two vectors divided by the product of the magnitudes of both vectors.

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

A.B = (1*0 + 1*0 + 1*1 + 1*1 + 1*0 + 0*1 + 0*1) = 2

||A|| = sqrt(1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 0^2 + 0^2) = sqrt(5)

||B|| = sqrt(0^2 + 0^2 + 1^2 + 1^2 + 0^2 + 1^2 + 1^2) = sqrt(4)

Cosine Similarity = 2 / (sqrt(5) * sqrt(4)) = 2 / (2.236067977 * 2) = 0.447213595

So, the cosine similarity of the two documents is approximately 0.447, which is closest to option 1. Therefore, the answer is 1. 0.44721.

Knowee AI · Accepted Answer