# TEST_NEAREST Test Functions for the Nearest Neighbor Calculation

TEST_NEAREST is a MATLAB program which tests several functions that carry out the nearest neighbor calculation.

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),
• JR = NEAREST(JS), the index of the point in R for which the distance D(S(JS),R(JR)) is minimized.

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.

Lloyd's version of the Centroidal Voronoi Tessellation (CVT) algorithm estimates the area or volume of the cells using sampling. This computation is a nearest neighbor calculation.

### Languages:

TEST_NEAREST is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

### Related Programs:

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.

NEAREST_NEIGHBOR, a MATLAB library 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.

### 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:

• find_closest1.m, a straightforward calculation which, for each sample point, computes the distance to each data point, and remembers the index of the closest one;
• find_closest2.m, a calculation which, for each sample point, uses the MATLAB commands repmat() and min(), hoping for faster execution.
• find_closest3.m, a calculation which, for each sample point, computes the distance vector using matrix algebra.
• nearest_neighbor.m, a function by Richard Brown for the nearest neighbor calculation.
• timestamp.m, prints the current YMDHMS date as a timestamp;

### Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 23 December 2012.