nncross.ppx: Nearest Neighbours Between Two Patterns in Any Dimensions

Description

Given two point patterns X and Y in many dimensional space, finds the nearest neighbour in Y of each point of X.

Usage

# S3 method for ppx
nncross(X, Y,
          iX=NULL, iY=NULL,
          what = c("dist", "which"),
          ...,
          k = 1)

Value

A data frame, or a vector if the data frame would contain only one column.

By default (if what=c("dist", "which") and k=1) a data frame with two columns:

dist: Nearest neighbour distance
which: Nearest neighbour index in Y

If what="dist" and k=1, a vector of nearest neighbour distances.

If what="which" and k=1, a vector of nearest neighbour indices.

If k is specified, the result is a data frame with columns containing the k-th nearest neighbour distances and/or nearest neighbour indices.

Arguments

X,Y: Point patterns in any number of spatial dimensions (objects of class "ppx").
iX, iY: Optional identifiers, used to determine whether a point in X is identical to a point in Y. See Details.
what: Character string specifying what information should be returned. Either the nearest neighbour distance ("dist"), the identifier of the nearest neighbour ("which"), or both.
k: Integer, or integer vector. The algorithm will compute the distance to the kth nearest neighbour.
...: Ignored.

Author

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

Details

Given two point patterns X and Y in $m$ -dimensional space, this function finds, for each point of X, the nearest point of Y. The distance between these points is also computed. If the argument k is specified, then the k-th nearest neighbours will be found.

The return value is a data frame, with rows corresponding to the points of X. The first column gives the nearest neighbour distances (i.e. the ith entry is the distance from the ith point of X to the nearest element of Y). The second column gives the indices of the nearest neighbours (i.e.\ the ith entry is the index of the nearest element in Y.) If what="dist" then only the vector of distances is returned. If what="which" then only the vector of indices is returned.

The argument k may be an integer or an integer vector. If it is a single integer, then the k-th nearest neighbours are computed. If it is a vector, then the k[i]-th nearest neighbours are computed for each entry k[i]. For example, setting k=1:3 will compute the nearest, second-nearest and third-nearest neighbours. The result is a data frame.

Note that this function is not symmetric in X and Y. To find the nearest neighbour in X of each point in Y, use nncross(Y,X).

The arguments iX and iY are used when the two point patterns X and Y have some points in common. In this situation nncross(X, Y) would return some zero distances. To avoid this, attach a unique integer identifier to each point, such that two points are identical if their identifying numbers are equal. Let iX be the vector of identifier values for the points in X, and iY the vector of identifiers for points in Y. Then the code will only compare two points if they have different values of the identifier. See the Examples.

Examples

Run this code

  XYZ <- ppx(matrix(runif(80), 20, 4),
            boxx(c(0,1), c(0,1), c(0,1), c(0,1)))

  ## two different point patterns
  X <- XYZ[1:5]
  Y <- XYZ[10:20]
  nncross(X,Y)
  N23 <- nncross(X,Y, k=2:3)

  ## two patterns with some points in common
  X <- XYZ[1:15]
  Y <- XYZ[10:20]
  iX <- 1:15
  iY <- 10:20
  N <- nncross(X,Y, iX, iY, what="which")
  N4 <- nncross(X,Y, iX, iY, k=4)

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