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//! See the [Crates.io page](https://crates.io/crates/space) for the README. #![no_std] doc_comment::doctest!("../README.md"); #[cfg(feature = "alloc")] extern crate alloc; #[cfg(feature = "serde")] use serde::{Deserialize, Serialize}; #[cfg(feature = "alloc")] use alloc::vec::Vec; use num_traits::Zero; /// This trait is implemented for metrics that form a metric space. /// It is primarily used for keys in nearest neighbor searches. /// When implementing this trait, it is recommended to choose the smallest unsigned integer that /// represents your metric space, but you may also use a float so long as you wrap it in /// a newtype that enforces the `Ord + Zero + Copy` trait bounds. /// It is recommended to use /// [`NoisyFloat`](https://docs.rs/noisy_float/0.2.0/noisy_float/struct.NoisyFloat.html) /// for this purpose, as it implements the trait bound. /// /// It is important that all metrics that implement this trait satisfy /// the [triangle inequality](https://en.wikipedia.org/wiki/Triangle_inequality). /// This requirement basically means that the sum of distances that start /// at a point A and end at a point B can never be less than the distance /// from A to B directly. Note that the metric is required to be an unsigned integer, /// as distances can only be positive and must be fully ordered. /// It is also required that two overlapping points (the same point in space) must return /// a distance of [`Zero::zero`]. /// /// Floating point numbers can be converted to integer metrics by being interpreted as integers by design, /// although some special patterns (like NaN) do not fit into this model. To be interpreted as an unsigned /// integer, the float must be positive zero, subnormal, normal, or positive infinity. Any NaN needs /// to be dealt with before converting into a metric, as they do NOT satisfy the triangle inequality, /// and will lead to errors. You may want to check for positive infinity as well depending on your use case. /// You must remove NaNs if you convert to integers, but you must also remove NaNs if you use an ordered /// wrapper like [`NoisyFloat`](https://docs.rs/noisy_float/0.2.0/noisy_float/struct.NoisyFloat.html). /// Be careful if you use a wrapper like /// [`FloatOrd`](https://docs.rs/float-ord/0.3.2/float_ord/struct.FloatOrd.html) which does not /// force you to remove NaNs. When implementing a metric, you must be sure that NaNs are not allowed, because /// they may cause nearest neighbor algorithms to panic. /// /// ## Example /// /// ``` /// struct AbsDiff; /// /// impl space::Metric<f64> for AbsDiff { /// type Unit = u64; /// /// fn distance(&self, &a: &f64, &b: &f64) -> Self::Unit { /// let delta = (a - b).abs(); /// debug_assert!(!delta.is_nan()); /// delta.to_bits() /// } /// } /// ``` pub trait Metric<P> { type Unit: Ord + Zero + Copy; fn distance(&self, a: &P, b: &P) -> Self::Unit; } /// For k-NN algorithms to return neighbors. #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] pub struct Neighbor<Unit, Ix = usize> { /// Index of the neighbor in the search space. pub index: Ix, /// The distance of the neighbor from the search feature. pub distance: Unit, } /// Implement this trait on data structures (or wrappers) which perform KNN searches. /// The data structure should maintain a key-value mapping between neighbour points and data /// values. /// /// The lifetime on the trait will be removed once GATs are stabilized. pub trait Knn<'a> { type Ix: Copy; type Point: 'a; type Value: 'a; type Metric: Metric<Self::Point>; type KnnIter: IntoIterator< Item = ( Neighbor<<Self::Metric as Metric<Self::Point>>::Unit, Self::Ix>, &'a Self::Point, &'a Self::Value, ), >; /// Get a point using a neighbor index returned by [`Knn::knn`] or [`Knn::nn`]. /// /// This should only be used directly after one of the mentioned methods are called to retrieve /// a point associated with a neighbor, and will panic if the index is incorrect due to /// mutating the data structure thereafter. The index is only valid up until the next mutation. fn point(&self, index: Self::Ix) -> &'a Self::Point; /// Get a value using a neighbor index returned by [`Knn::knn`] or [`Knn::nn`]. /// /// This should only be used directly after one of the mentioned methods are called to retrieve /// a value associated with a neighbor, and will panic if the index is incorrect due to /// mutating the data structure thereafter. The index is only valid up until the next mutation. fn value(&self, index: Self::Ix) -> &'a Self::Value; /// Get `num` nearest neighbor keys and values of `target`. /// /// For many KNN search algorithms, the returned neighbors are approximate, and may not /// be the actual nearest neighbors. fn knn(&'a self, query: &Self::Point, num: usize) -> Self::KnnIter; /// Get the nearest neighbor key and values of `target`. /// /// For many KNN search algorithms, the returned neighbors are approximate, and may not /// be the actual nearest neighbors. #[allow(clippy::type_complexity)] fn nn( &'a self, query: &Self::Point, ) -> Option<( Neighbor<<Self::Metric as Metric<Self::Point>>::Unit, Self::Ix>, &'a Self::Point, &'a Self::Value, )>; } /// Implement this trait on data structures (or wrappers) which perform range queries. /// The data structure should maintain a key-value mapping between neighbour points and data /// values. /// /// The lifetime on the trait will be removed once GATs are stabilized. pub trait RangeQuery<'a>: Knn<'a> { type RangeIter: IntoIterator< Item = ( Neighbor<<Self::Metric as Metric<Self::Point>>::Unit, Self::Ix>, &'a Self::Point, &'a Self::Value, ), >; /// Get all the points in the data structure that lie within a specified range of the query /// point. The points may or may not be sorted by distance. #[allow(clippy::type_complexity)] fn range_query( &self, query: &Self::Point, range: <Self::Metric as Metric<Self::Point>>::Unit, ) -> Self::RangeIter; } /// Implement this trait on KNN search data structures that map keys to values and which you can /// insert new (key, value) pairs. pub trait KnnInsert<'a>: Knn<'a> { /// Insert a (key, value) pair to the [`KnnMap`]. /// /// Returns the index type fn insert(&mut self, key: Self::Point, value: Self::Value) -> Self::Ix; } /// Create a data structure from a metric and a batch of data points, such as a vector. /// For many algorithms, using batch initialization yields better results than inserting the points /// one at a time. pub trait KnnFromMetricAndBatch<M, B> { fn from_metric_and_batch(metric: M, batch: B) -> Self; } /// Create a data structure from a batch of data points, such as a vector. /// For many algorithms, using batch initialization yields better results than inserting the points /// one at a time. pub trait KnnFromBatch<M, B>: KnnFromMetricAndBatch<M, B> { fn from_batch(batch: B) -> Self; } impl<M, B, T> KnnFromBatch<M, B> for T where T: KnnFromMetricAndBatch<M, B>, M: Default, { fn from_batch(batch: B) -> Self { Self::from_metric_and_batch(M::default(), batch) } } /// Performs a linear knn search by iterating over everything in the space /// and performing a binary search on running set of neighbors. /// /// ## Example /// /// ``` /// use space::{Knn, LinearKnn, Metric, Neighbor, KnnFromBatch}; /// /// #[derive(Default)] /// struct Hamming; /// /// impl Metric<u8> for Hamming { /// type Unit = u8; /// /// fn distance(&self, &a: &u8, &b: &u8) -> Self::Unit { /// (a ^ b).count_ones() as u8 /// } /// } /// /// let data = vec![ /// (0b1010_1010, 12), /// (0b1111_1111, 13), /// (0b0000_0000, 14), /// (0b1111_0000, 16), /// (0b0000_1111, 10), /// ]; /// /// let search: LinearKnn<Hamming, _> = KnnFromBatch::from_batch(data.iter()); /// /// assert_eq!( /// &search.knn(&0b0101_0000, 2), /// &[ /// (Neighbor { index: 2, distance: 2 }, &data[2].0, &data[2].1), /// (Neighbor { index: 3, distance: 2 }, &data[3].0, &data[3].1), /// ] /// ); /// ``` #[cfg(feature = "alloc")] pub struct LinearKnn<M, I> { pub metric: M, pub points: I, } #[cfg(feature = "alloc")] impl<'a, M: Metric<P>, I, P: 'a, V: 'a> Knn<'a> for LinearKnn<M, I> where I: Iterator<Item = &'a (P, V)> + Clone, { type Ix = usize; type Metric = M; type Point = P; type Value = V; type KnnIter = Vec<(Neighbor<M::Unit>, &'a P, &'a V)>; fn point(&self, index: Self::Ix) -> &'a Self::Point { &self.points.clone().nth(index).unwrap().0 } fn value(&self, index: Self::Ix) -> &'a Self::Value { &self.points.clone().nth(index).unwrap().1 } fn knn(&'a self, query: &Self::Point, num: usize) -> Self::KnnIter { // Create an iterator mapping the dataset into `Neighbor`. let mut dataset = self.points.clone().enumerate().map(|(index, (pt, val))| { ( Neighbor { index, distance: self.metric.distance(pt, query), }, pt, val, ) }); // Create a vector with the correct capacity in advance. let mut neighbors = Vec::with_capacity(num); // Extend the vector with the first `num` neighbors. neighbors.extend((&mut dataset).take(num)); // Sort the vector by the neighbor distance. neighbors.sort_unstable_by_key(|n| n.0.distance); // Iterate over each additional neighbor. for point in dataset { // Find the position at which it would be inserted. let position = neighbors.partition_point(|n| n.0.distance <= point.0.distance); // If the point is closer than at least one of the points already in `neighbors`, add it // into its sorted position. if position != num { neighbors.pop(); neighbors.insert(position, point); } } neighbors } #[allow(clippy::type_complexity)] fn nn( &self, query: &Self::Point, ) -> Option<( Neighbor<<Self::Metric as Metric<Self::Point>>::Unit, Self::Ix>, &'a Self::Point, &'a Self::Value, )> { // Map the input iterator into neighbors and then find the smallest one by distance. self.points .clone() .enumerate() .map(|(index, (pt, val))| { ( Neighbor { index, distance: self.metric.distance(pt, query), }, pt, val, ) }) .min_by_key(|n| n.0.distance) } } #[cfg(feature = "alloc")] impl<'a, M, I> KnnFromMetricAndBatch<M, I> for LinearKnn<M, I> where M: Default, { fn from_metric_and_batch(metric: M, points: I) -> Self { Self { metric, points } } }