nearest_neighbor

nearest_neighbor, a MATLAB code which is given two sets of M-dimensional points R and S; For each point in S, it finds the closest point in R. The code is by Richard Brown.

In a nearest neighbor calculation, we are given:

  • R, a set of NR points in M dimensions.
  • S, a set of NS points in M dimensions.
  • D(x,y), a norm for measuring distances between points in M dimensions.

    • and we are asked to compute, for each point S(JS),

    Obviously, one method to determine the values in NEAREST is simply to compute every distance and take the index of the minimum. But even this simple idea can be implemented in many ways in MATLAB, and implementations will vary in their cost in memory and time.

    Also, note that if the dimension M is small, and if the size of the R set is small relative to that of S, it may be much cheaper to compute the Delaunay triangulation of R (or its higher-dimensional generalization). Computing the triangulation is somewhat expensive, but makes the search procedure extremely quick.

    Richard Brown's function tries to use MATLAB's Delaunay search algorithm when it seems preferable, and otherwise computes the nearest neighbor by the straightforward approach.

    Licensing:

    Copyright (c) 2009, Richard Brown. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted if accompanied by the following disclaimer: 

         
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
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    Languages:

    nearest_neighbor is available in a MATLAB version.

    Related Programs:

    nearest_neighbor_test

    closest_point_brute, a MATLAB code which tests the time complexity of various procedures for solving the nearest neighbor problem.

    cvt, a MATLAB code which computes elements of a Centroidal Voronoi Tessellation (CVT).

    nearest_interp_1d, a MATLAB code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

    References:

    1. Sunil Arya, David Mount, Nathan Netanyahu, Ruth Silverman, Angela Wu,
      An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions,
      Journal of the ACM,
      Volume 45, Number 6, November 1998, pages 891-923.
    2. Jon Bentley, Bruce Weide, Andrew Yao,
      Optimal Expected Time Algorithms for Closest Point Problems,
      ACM Transactions on Mathematical Software,
      Volume 6, Number 4, December 1980, pages 563-580.
    3. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
      Computational Geometry,
      Springer, 2000,
      ISBN: 3-540-65620-0,
      LC: QA448.D38.C65.

    Source Code:

    Last revised on 17 August 2024.