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I have two vectors

Vector1(1,2,3,4,5,6)

Vector2(12,13,14,15,16,17)

Two vectors is completely different. But i used Cosine Similarity formula and the result is 0.943843313096.

I think result is about 0,1 or 0,2... but not. Why? please explain for me, thanks so much.

Community
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atimetoremember
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2 Answers2

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If you reduce the vectors to 2 dimensions you can understand it better.

Vector1(1,2) and Vector2(12,13)

The position vector1 will make an angle of 63.5 Degrees and position vector2 will make an angle of 47.31 degrees. The difference is only 16.1 degrees. Cos(16.1) = 0.96081

  • The usual way to look at the cosine distance is Cos(theta) = A.B/(Norm(A)*Norm(B)) for the above vectors, A.B = 38 Norm(A) = 2.23, Norm(B) = 17.69 So, Cos(theta) = 38/(2.23*17.69) = 0.96056

If you find theta from the above, theta will be equal to 16.1 degrees !!!

narasimman
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0

Cosine similarity is a measure of the angle difference between the vectors. Those vectors point in a similar direction, so the cosine being close to 1 is expected.

muzzlator
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