# Cosine Similarity - [Lp Regularization](Lp%20Regularization.md) l2norm aka p = 2 - $S_{c}(A,B) := cos(\theta) = \frac{A\cdot B}{||A|| ||B||} = \frac{\Sigma_{i=1}^{n}A_{i}B_{i}}{\sqrt{\Sigma_{i=1}^{n}A^{2}_{i}} \sqrt{\Sigma_{i=1}^{n}B_{i}^{2}}}$ - ranges from -1 : exactly opposite, 1 : exactly same, 0: orthogonal/not correlated, intermediate - [Cosine Distance](Cosine Distance.md) - Cosine similarity is $ - \mathrm{sum}\left( \mathrm{l2norm}\left( y \right) \cdot \mathrm{l2norm}\left( ŷ \right) \right)$ -  - magnitude of vectors is not taken into account, merely their direction - In practice, this means that the differences in values are not fully taken into account - If you take a [Recommender System](Recommender%20System.md), for example, then the cosine similarity does not take into account the difference in rating scale between different users - high-dimensional data and when the magnitude of the vectors is not of importance