diff options
Diffstat (limited to 'src/cos.rs')
| -rw-r--r-- | src/cos.rs | 56 |
1 files changed, 54 insertions, 2 deletions
@@ -12,8 +12,16 @@ use std::cmp::Ordering; /// /// Use [cosine_distance] instead if you are implementing [Proximity::distance()]. /// +/// ```math +/// \begin{aligned} +/// \mathrm{cosine\_similarity}(x, y) &= \frac{x \cdot y}{\|x\| \|y\|} \\ +/// &= \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2} \sqrt{\sum_i y_i^2}} \\ +/// &= \cos \theta +/// \end{aligned} +/// ``` +/// /// [cosine *similarity*]: https://en.wikipedia.org/wiki/Cosine_similarity -/// [Proximity::distance()]: Proximity#method.distance +/// [Proximity::distance()]: Proximity#tymethod.distance pub fn cosine_similarity<T, U>(x: T, y: U) -> T::Value where T: Coordinates, @@ -39,6 +47,15 @@ where /// Compute the [cosine distance] between two points. /// +/// ```math +/// \begin{aligned} +/// \mathrm{cosine\_distance}(x, y) &= 1 - \mathrm{cosine\_similarity}(x, y) \\ +/// &= 1 - \frac{x \cdot y}{\|x\| \|y\|} \\ +/// &= 1 - \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2} \sqrt{\sum_i y_i^2}} \\ +/// &= 1 - \cos \theta +/// \end{aligned} +/// ``` +/// /// [cosine distance]: https://en.wikipedia.org/wiki/Cosine_similarity pub fn cosine_distance<T, U>(x: T, y: U) -> T::Value where @@ -97,8 +114,16 @@ where /// /// Use [prenorm_cosine_distance] instead if you are implementing [Proximity::distance()]. /// +/// ```math +/// \begin{aligned} +/// \mathrm{prenorm\_cosine\_similarity}(x, y) &= x \cdot y \\ +/// &= \sum_i x_i y_i \\ +/// &= \cos \theta +/// \end{aligned} +/// ``` +/// /// [cosine *similarity*]: https://en.wikipedia.org/wiki/Cosine_similarity -/// [`Proximity::distance()`]: Proximity#method.distance +/// [`Proximity::distance()`]: Proximity#tymethod.distance pub fn prenorm_cosine_similarity<T, U>(x: T, y: U) -> T::Value where T: Coordinates, @@ -118,6 +143,15 @@ where /// Compute the [cosine distance] between two pre-normalized (unit magnitude) points. /// +/// ```math +/// \begin{aligned} +/// \mathrm{prenorm\_cosine\_distance}(x, y) &= 1 - \mathrm{prenorm\_cosine\_similarity}(x, y) \\ +/// &= 1 - x \cdot y \\ +/// &= 1 - \sum_i x_i y_i \\ +/// &= 1 - \cos \theta +/// \end{aligned} +/// ``` +/// /// [cosine distance]: https://en.wikipedia.org/wiki/Cosine_similarity pub fn prenorm_cosine_distance<T, U>(x: T, y: U) -> T::Value where @@ -175,6 +209,15 @@ where /// Compute the [angular distance] between two points. /// +/// ```math +/// \begin{aligned} +/// \mathrm{angular\_distance}(x, y) &= \arccos(\mathrm{cosine\_similarity}(x, y)) \\ +/// &= \arccos \left( \frac{x \cdot y}{\|x\| \|y\|} \right) \\ +/// &= \arccos \left( \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2} \sqrt{\sum_i y_i^2}} \right) \\ +/// &= \theta +/// \end{aligned} +/// ``` +/// /// [angular distance]: https://en.wikipedia.org/wiki/Cosine_similarity#Angular_distance_and_similarity pub fn angular_distance<T, U>(x: T, y: U) -> AngularDistance<T::Value> where @@ -257,6 +300,15 @@ where /// Compute the [angular distance] between two points. /// +/// ```math +/// \begin{aligned} +/// \mathrm{prenorm\_angular\_distance}(x, y) &= \arccos(\mathrm{prenorm\_cosine\_similarity}(x, y)) \\ +/// &= \arccos(x \cdot y) \\ +/// &= \arccos \left( \sum_i x_i y_i \right) \\ +/// &= \theta +/// \end{aligned} +/// ``` +/// /// [angular distance]: https://en.wikipedia.org/wiki/Cosine_similarity#Angular_distance_and_similarity pub fn prenorm_angular_distance<T, U>(x: T, y: U) -> AngularDistance<T::Value> where |