acap

As Close As Possible — nearest neighbor search in Rust.

Example

use acap::euclid::Euclidean;
use acap::vp::VpTree;
use acap::NearestNeighbors;

let tree = VpTree::balanced(vec![
    Euclidean([3, 4]),
    Euclidean([5, 12]),
    Euclidean([8, 15]),
    Euclidean([7, 24]),
]);

let nearest = tree.nearest(&[7, 7]).unwrap();
assert_eq!(nearest.item, &Euclidean([3, 4]));
assert_eq!(nearest.distance, 5);

lib.rs:

As Close As Possible — nearest neighbor search in Rust.

Overview

The notion of distances between points is captured by the Proximity trait. Its distance() method returns a Distance, from which the actual numerical distance may be retrieved with value(). These layers of abstraction allow acap to work generically with different distance functions over different types.

There are no restrictions on the distances computed by a Proximity. For example, they don't have to be symmetric, subadditive, or even positive. Implementations that do have these desirable properties will additionally implement the Metric marker trait. This distinction allows acap to support a wide variety of useful metric and non-metric distances.

As a concrete example, consider Euclidean<[i32; 2]>. The Euclidean wrapper equips any type that has coordinates with the Euclidean distance function as its Proximity implementation:

 use acap::distance::Proximity;
 use acap::euclid::Euclidean;

 let a = Euclidean([3, 4]);
 let b = Euclidean([7, 7]);
 assert_eq!(a.distance(&b), 5);

In this case, distance() doesn't return a number directly; as an optimization, it returns a EuclideanDistance wrapper. This wrapper stores the squared value of the distance, to avoid computing square roots until absolutely necessary. Still, it transparently supports comparisons with numerical values:

 # use acap::distance::Proximity;
 # use acap::euclid::Euclidean;
 # let a = Euclidean([3, 4]);
 # let b = Euclidean([7, 7]);
 use acap::distance::Distance;

 let d = a.distance(&b);
 assert!(d > 4 && d < 6);
 assert_eq!(d, 5);
 assert_eq!(d.value(), 5.0f32);

For finding the nearest neighbors to a point from a set of other points, the NearestNeighbors trait provides a uniform interface to many different similarity search data structures. One such structure is the vantage-point tree, available in acap as VpTree:

 # use acap::euclid::Euclidean;
 use acap::vp::VpTree;

 let tree = VpTree::balanced(vec![
     Euclidean([3, 4]),
     Euclidean([5, 12]),
     Euclidean([8, 15]),
     Euclidean([7, 24]),
 ]);

VpTree implements NearestNeighbors, which has a nearest() method that returns an optional Neighbor. The Neighbor struct holds the actual neighbor it found, and the distance it was from the target:

 # use acap::euclid::Euclidean;
 # use acap::vp::VpTree;
 use acap::knn::NearestNeighbors;

 # let tree = VpTree::balanced(
 #     vec![Euclidean([3, 4]), Euclidean([5, 12]), Euclidean([8, 15]), Euclidean([7, 24])]
 # );
 let nearest = tree.nearest(&[7, 7]).unwrap();
 assert_eq!(nearest.item, &Euclidean([3, 4]));
 assert_eq!(nearest.distance, 5);

NearestNeighbors also provides the nearest_within(), k_nearest(), and k_nearest_within() methods which find up to k neighbors within a possible threshold.

It can be expensive to compute nearest neighbors exactly, especially in high dimensions. For performance reasons, NearestNeighbors implementations are allowed to return approximate results. Many implementations have a speed/accuracy tradeoff which can be tuned. Those implementations which always return exact results will also implement the ExactNeighbors marker trait. For example, a VpTree will be exact when the Proximity function is a Metric.

Examples

Searching without owning

Since Proximity has a blanket implementation for references, you can store references in a nearest neighbor index instead of having it hold the data itself:

 use acap::euclid::Euclidean;
 use acap::knn::NearestNeighbors;
 use acap::vp::VpTree;

 let points = vec![
     Euclidean([3, 4]),
     Euclidean([5, 12]),
     Euclidean([8, 15]),
     Euclidean([7, 24]),
 ];

 let tree = VpTree::balanced(points.iter());

 let nearest = tree.nearest(&&[7, 7]).unwrap();
 assert!(std::ptr::eq(*nearest.item, &points[0]));

Custom distance functions

See the Proximity documentation.