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kd-trees in Clojure

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README.md

clj-kdtree

Overview

A Kd-tree is a special type of binary tree that partitions points in a k-dimensional space. It can be used for efficient nearest-neighbor searches.

For more detail, refer to Wikipedia on Kd-trees.

Usage

Add this to your project.clj :dependencies list:

[clj-kdtree "1.2.0]

Build

(require 'kdtree)

(def points [[8 8] [3 1] [6 6] [7 7] [1 3] [4 4] [5 5]])
;; Build a kdtree from a set of points
(def tree (kdtree/build-tree points))
(println "Tree:" tree)

Nearest neighbor

Use tree to find neighbors for one point given a set of points:

(println "Four points closest to [2 2]:\n"
         (kdtree/nearest-neighbor tree [2 2] 4))

output:

Four points closest to [2 2]:
 (#kdtree.Result{:point [1.0 3.0], :dist-squared 2.0}
  #kdtree.Result{:point [3.0 1.0], :dist-squared 2.0}
  #kdtree.Result{:point [4.0 4.0], :dist-squared 8.0}
  #kdtree.Result{:point [5.0 5.0], :dist-squared 18.0})

Interval search

Find all points inside interval:

(println "Points 1≤x≤4, 3≤y≤6\n"
         (kdtree/interval-search tree [[1 4] [3 6]]))

output:

Points 1≤x≤4, 3≤y≤6
 [[1.0 3.0] [4.0 4.0]]

Delete

Delete point and return new version of a tree. Doesn't change old tree.

(println "Four points with deletion:\n"
         (-> tree
             (kdtree/delete [1 3])
             (kdtree/delete [3 1])
             (kdtree/nearest-neighbor [2 2] 4)))

output:

Four points with deletion:
 (#kdtree.Result{:point [4.0 4.0], :dist-squared 8.0}
  #kdtree.Result{:point [5.0 5.0], :dist-squared 18.0}
  #kdtree.Result{:point [6.0 6.0], :dist-squared 32.0}
  #kdtree.Result{:point [7.0 7.0], :dist-squared 50.0})

Insert

Insert point and return new version of a tree. Doesn't change old tree.

(println "\n\nFour points with insertion:\n"
         (-> tree
             (kdtree/insert [1.5 1.5])
             (kdtree/nearest-neighbor [2 2] 4)))

output:

Four points with insertion:
 (#kdtree.Result{:point [1.5 1.5], :dist-squared 0.5}
  #kdtree.Result{:point [3.0 1.0], :dist-squared 2.0}
  #kdtree.Result{:point [1.0 3.0], :dist-squared 2.0}
  #kdtree.Result{:point [4.0 4.0], :dist-squared 8.0})

Metadata

To store arbitrary information in points you can use metadata attached to the points. All tree modification operations like build-tree, insert and delete retain metadata. All query operation like nearest-neighbor and interval-search return points with corresponded meta:

(def point (with-meta [0 0] {:value "Hello"}))
(def tree (kdtree/build-tree [point]))
(println "Meta:"
         (meta (kdtree/nearest-neighbor tree [1 1])))

output:

Meta: {:value Hello}

License

Copyright (C) 2009-2013 Brendan Ribera and contributors. All rights reserved.

Distributed under the MIT License; see the file LICENSE at the root of this distribution.

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