NEAREST_NEIGHBOR is a MATLAB function which works in a given M-dimensional space, seeking, for each point in a set S, the nearest point in a set R, by Richard Brown.
In a nearest neighbor calculation, we are given:
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.
Copyright (c) 2009, Richard Brown All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
NEAREST_NEIGHBOR is available in a MATLAB version.
CVT, a MATLAB library which computes elements of a Centroidal Voronoi Tessellation (CVT).
NEAREST_INTERP_1D, a MATLAB library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.
TEST_NEAREST, a MATLAB program which tests the time complexity of various procedures for solving the nearest neighbor problem.
You can go up one level to the MATLAB source codes.