Table 2. Techniques for measuring the similarity between two vectors u and v of size d.

Similarity between the two vectors has an inverse relationship with metric value in a “decreasing” relationship, such as Euclidean distance.

Similarity Technique	Description	Relation	Formula
Euclidean distance	Length of the line between ends of vectors	Decreasing	$\sqrt{{\left(u_1-v_1\right)}^2+{\left(u_2-v_2\right)}^2+\dots +{\left(u_d-v_d\right)}^2}$
Cosine similarity	Cosine of the angle between vectors ($\theta$)	Increasing	$\frac{u^{T}v}{\left|u\right|.\left|v\right|}$
Dot product	Cosine $\theta$ multiplied by lengths of the vectors	Increasing	$u_1{v}_1+u_2{v}_2+\dots +u_d{v}_d=\left|u\right|\left|v\right| cos\left(\theta \right)$