about cosine similarity

Question

hi i m finding cosine similarity between documents ..i did like dis

D1=(8,0,0,1) where 8,0,0,1 are the tf-idf scores of the terms t1, t2, t3 , t4

D2=(7,0,0,1)

cos(theta) = (56 + 0 + 0 + 1) / sqrt(64 + 49) sqrt(1 +1 )

which comes out to be

cos(theta)= 5

now what do i evaluate from this value...i dont get it wat does cos(theta)=5 signify about the similarity between them...pls reply ..Am i doing things right ??????????..pls do reply guys.. will be thank ful to you..

Answer 1

The denominator is wrong.

The cosine similarity is defined as

         D1 · D2
 sim = ———————————
        |D1| |D2|

Here

D1 · D2 = (7*8 + 0*0 + 0*0 + 1*1) = 57
           ______________________    __
   |D2| = √ 7^2 + 0^2 + 0^2 + 1^2 = √50
           ______________________    __
   |D1| = √ 8^2 + 0^2 + 0^2 + 1^2 = √65

So the similarity should be (57 / √(50 * 65)) = 0.999846142, not 5.