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# Cosine#

Cosine Similarity is a measure that ignores the magnitude of the distance between two non-zero vectors thus acting as strictly a judgement of orientation. Two vectors with the same orientation have a cosine similarity of 1, whereas two vectors oriented at 90° relative to each other have a similarity of 0, and two vectors diametrically opposed have a similarity of -1. To be used as a distance function, we subtract the Cosine Similarity from 1 in order to satisfy the positive semi-definite condition, therefore the Cosine distance is a number between 0 and 2.

${\displaystyle {\text{Cosine}}=1 - {\mathbf {A} \cdot \mathbf {B} \over \|\mathbf {A} \|\|\mathbf {B} \|}=1 - {\frac {\sum \limits _{i=1}^{n}{A_{i}B_{i}}}{{\sqrt {\sum \limits _{i=1}^{n}{A_{i}^{2}}}}{\sqrt {\sum \limits _{i=1}^{n}{B_{i}^{2}}}}}}}$

Data Type Compatibility: Continuous

## Parameters#

This kernel does not have any parameters.

## Example#

use Rubix\ML\Kernels\Distance\Cosine;

\$kernel = new Cosine();