Cosine similarity

$$sim_{cos}(\vec{x} , \vec{y}) = \cos\theta = \frac{\vec{x} \cdot \vec{y} }{\parallel \vec{x} \parallel \parallel \vec{y} \parallel} = \frac{\sum^n_{i=1} x_iy_i}{\sqrt{ \sum^n_{i=1} x_i^2 } \sqrt{ \sum^n_{i=1} y_i^2 }}$$