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//! [Cosine distance](https://en.wikipedia.org/wiki/Cosine_similarity).
use crate::coords::Coordinates;
use crate::distance::{Metric, Proximity};
use num_traits::real::Real;
use num_traits::{one, zero};
/// Compute the [cosine *similarity*] between two points.
///
/// This is not suitable for implementing [`Proximity::distance()`] because the result is reversed
///
/// [cosine *similarity*]: https://en.wikipedia.org/wiki/Cosine_similarity
/// [`Proximity::distance()`]: Proximity#method.distance
pub fn cosine_similarity<T, U>(x: T, y: U) -> T::Value
where
T: Coordinates,
U: Coordinates<Value = T::Value>,
T::Value: Real,
{
debug_assert!(x.dims() == y.dims());
let mut dot: T::Value = zero();
let mut xx: T::Value = zero();
let mut yy: T::Value = zero();
for i in 0..x.dims() {
let xi = x.coord(i);
let yi = y.coord(i);
dot += xi * yi;
xx += xi * xi;
yy += yi * yi;
}
dot / (xx * yy).sqrt()
}
/// Compute the [cosine distance] between two points.
///
/// [cosine distance]: https://en.wikipedia.org/wiki/Cosine_similarity
pub fn cosine_distance<T, U>(x: T, y: U) -> T::Value
where
T: Coordinates,
U: Coordinates<Value = T::Value>,
T::Value: Real,
{
let one: T::Value = one();
one - cosine_similarity(x, y)
}
/// Equips any [coordinate space] with the [cosine distance] function.
///
/// [coordinate space]: [Coordinates]
/// [cosine distance]: https://en.wikipedia.org/wiki/Cosine_similarity
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub struct Cosine<T>(pub T);
impl<T> Proximity for Cosine<T>
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &Self) -> Self::Distance {
cosine_distance(&self.0, &other.0)
}
}
impl<T> Proximity<T> for Cosine<T>
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &T) -> Self::Distance {
cosine_distance(&self.0, other)
}
}
impl<T> Proximity<Cosine<T>> for T
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &Cosine<T>) -> Self::Distance {
cosine_distance(self, &other.0)
}
}
/// Compute the [angular distance] between two points.
///
/// [angular distance]: https://en.wikipedia.org/wiki/Cosine_similarity#Angular_distance_and_similarity
pub fn angular_distance<T, U>(x: T, y: U) -> T::Value
where
T: Coordinates,
U: Coordinates<Value = T::Value>,
T::Value: Real,
{
cosine_similarity(x, y).acos()
}
/// Equips any [coordinate space] with the [angular distance] metric.
///
/// [coordinate space]: [Coordinates]
/// [angular distance]: https://en.wikipedia.org/wiki/Cosine_similarity#Angular_distance_and_similarity
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub struct Angular<T>(pub T);
impl<T> Proximity for Angular<T>
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &Self) -> Self::Distance {
cosine_distance(&self.0, &other.0)
}
}
impl<T> Proximity<T> for Angular<T>
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &T) -> Self::Distance {
angular_distance(&self.0, other)
}
}
impl<T> Proximity<Angular<T>> for T
where
T: Coordinates,
T::Value: Real,
{
type Distance = T::Value;
fn distance(&self, other: &Angular<T>) -> Self::Distance {
angular_distance(self, &other.0)
}
}
/// Angular distance is a metric.
impl<T> Metric for Angular<T>
where
T: Coordinates,
T::Value: Real,
{}
/// Angular distance is a metric.
impl<T> Metric<T> for Angular<T>
where
T: Coordinates,
T::Value: Real,
{}
/// Angular distance is a metric.
impl<T> Metric<Angular<T>> for T
where
T: Coordinates,
T::Value: Real,
{}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_cosine() {
assert_eq!(cosine_distance([3.0, 4.0], [3.0, 4.0]), 0.0);
assert_eq!(cosine_distance([3.0, 4.0], [-4.0, 3.0]), 1.0);
assert_eq!(cosine_distance([3.0, 4.0], [-3.0, -4.0]), 2.0);
assert_eq!(cosine_distance([3.0, 4.0], [4.0, -3.0]), 1.0);
}
#[test]
fn test_angular() {
use std::f64::consts::{FRAC_PI_2, FRAC_PI_4, PI};
assert_eq!(angular_distance([3.0, 4.0], [3.0, 4.0]), 0.0);
assert!((angular_distance([3.0, 4.0], [-4.0, 3.0]) - FRAC_PI_2).abs() < 1.0e-9);
assert!((angular_distance([3.0, 4.0], [-3.0, -4.0]) - PI).abs() < 1.0e-9);
assert!((angular_distance([3.0, 4.0], [4.0, -3.0]) - FRAC_PI_2).abs() < 1.0e-9);
assert!((angular_distance([0.0, 1.0], [1.0, 1.0]) - FRAC_PI_4).abs() < 1.0e-9);
}
}
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