Details and Options

• Nearest works for a variety of data, including numerical, geospatial, textual, and visual, as well as dates and times.
• The data can also be given as an association. In this case, Nearest[<|key₁val₁,key₂val₂,…|>] is equivalent to Nearest[{val₁key₁,val₂key₂,…}].
• In Nearest[{elem₁,elem₂,…}prop,…], possible forms for prop include:
• "Element"the elem_i found to be nearest "Index"the index i of the elem_i found to be nearest "Distance"the distance to the nearest elem_i {prop₁,prop₂,…}a list of multiple forms Allan association giving element, index and distance
• When Nearest returns several elements elem_i, the nearest ones are given first.
• If several elements are at the same distance, they are returned in the order they appear in data.
• Nearest[data,x,{All,r}] can be used to get all elem_i within radius r.
• The following options can be given:
• DistanceFunction Automaticthe distance metric to use Method Automaticmethod to use WorkingPrecision Automaticprecision to use for numeric data
• By default, the following distance functions are used for different types of elem_i:
• Norm[#1-#2]&numeric data JaccardDissimilarityBoolean data EditDistancestrings ColorDistancecolors ImageDistanceimages DateDifferencedates and times GeoDistancegeospatial data
• Nearest with geospatial data uses GeoDistance to compute distances. The data can be given as a list of GeoPosition objects, or a GeoPosition containing an array of points.
• For images or colors and a distance function f, DistanceFunction->f is passed to ImageDistance and ColorDistance, respectively. »
• All images are conformed using ConformImages. With DistanceFunction->Automatic, dimensionality reduction based on discrete cosine transform is applied to the set of images.
• Using Norm[#1-#2,p]& for or named distance functions such as ManhattanDistance, ChessboardDistance, and EuclideanDistance can invoke special optimizations for numeric vector data.
• Possible settings for Method include "Octree", "KDtree", and "Scan".
• Possible settings for the WorkingPrecision option are:
• MachinePrecisionuse machine-precision numbers puse precision p Automaticuse adaptive precision to resolve nearest points

Examples

Basic Examples  (5)

Find the element nearest to 20:

Find the 3 elements nearest to 20:

Find which element is nearest to {2,3} in 2D:

Find "nearest" strings:

Find nearest colors:

Find the nearest image partition to a subimage:

Scope  (9)

Give the 3 nearest elements:

Give the elements within radius 2:

Give at most 3 nearest elements within radius 2:

Find the nearest matrix:

Find which element is nearest to {2,3} in 2D and return the appropriate label:

Compute the same using an Association:

Return the index for the nearest string:

Return an Association giving the string element, index, and distance:

Find the 3 elements nearest to 20, simultaneously reporting the elements and their distance to 20:

For uniform random points in 3D, give the distances for the 10 nearest to the origin:

For each of the 10 nearest, give an Association including the point element, index and distance:

Create a lookup function for future use:

Find the date nearest to a given DateObject:

Find out which of these {lat,lon} points on Earth is closest to you:

Express the input as a list of separate GeoPosition objects instead:

Report simultaneously the closest point and the distance to it:

Options  (6)

DistanceFunction  (3)

By default, normal Euclidean distance is used for points:

Use the ManhattanDistance, which sums the length of each side:

The ChessboardDistance only takes into account the dimension with the largest separation:

The DistanceFunction can be given as a symbol:

Or as a pure function:

Find nearest colors using a color distance different from the default distance in ColorDistance:

Method  (2)

Compare different methods for machine-precision data:

In three dimensions, the "KDtree" method is faster:

In 20 dimensions, a simple scan is faster:

The setting Method->{"KDtree","LeafSize"->s} may be used to control the maximum number of points in any leaf of the KD tree constructed:

Plot the tree setup time:

Plot the lookup time for different points:

WorkingPrecision  (1)

Using WorkingPrecision->MachinePrecision ensures the fastest evaluation method is used:

The results may not be correct if the numbers are not all distinct to machine precision:

All the points are effectively the same to machine precision:

An appropriate higher value of precision will work:

Applications  (8)

Plot the Nearest of a list of:

Create a Voronoi diagram:

Use higher resolution:

Use a 1-norm ("taxicab distance"):

Highlight the 200 random points closest to the origin:

Use the "taxicab" metric:

Create a nearest function from all the words in a dictionary:

Look up words closest to a given word:

Go farther:

Find the outputs from running a sequence of elementary cellular automata:

Generate a complete list of outputs from all 256 elementary cellular automata:

Find which rules give outputs nearest the specified sequences:

Use a negative distance function to find the element farthest away from the given element:

Show the returned element for all values between 1 and 5:

Take the polygon of Mexico:

Compute the nearest of the points of that polygon from your current geo location:

Draw the geodesic from your location to that point:

Properties & Relations  (2)

In the case of a tie, all nearest elements are returned in order:

The single argument form of Nearest returns a NearestFunction object:

This is an optimized lookup function, which is faster than calling Nearest repeatedly:

Neat Examples  (1)

Find successive nearest words in a dictionary: