Cosine similarity

For two vectors $u, v$ , we define the cosine angle between both vectors as:

c o s (u, v) = \frac{⟨ u, v ⟩}{| | u | | | | v | |}

This formula verifies:

c o s (u, v) = {\begin{cases} 1 & if u = v \\ - 1 & if u = - v \\ 0 & if u and v are orthogonal \end{cases}

A value close to 1 (resp. -1) indicate 2 vectors carrying a similar (resp. opposite) semantic meaning. A value of 0 indicates two uncorrelated words.