# Data Mining - Cosine Similarity (Measure of Angle)

## 1 - About

The cosine similarity is a measure of the angle between two vectors, normalized by magnitude. You just divide the dot product by the magnitude of the two vectors.

By taking the algebraic and geometric definition of the dot product, we get the cosine similarity that is a normalized dot product of two vectors $$similarity = \cos \theta = \frac{a.b}{||a|| ||b||} = \frac{ \sum a_i b_i }{ \sqrt{\sum a_i^2} \sqrt{\sum b_i^2} }$$