# nnwhich

0th

Percentile

##### Nearest neighbour

Finds the nearest neighbour of each point in a point pattern.

Keywords
spatial, math
##### Usage
nnwhich(X, …)
# S3 method for ppp
nnwhich(X, …, k=1, by=NULL, method="C")
# S3 method for default
nnwhich(X, Y=NULL, …, k=1, by=NULL, method="C")
##### Arguments
X,Y

Arguments specifying the locations of a set of points. For nnwhich.ppp, the argument X should be a point pattern (object of class "ppp"). For nnwhich.default, typically X and Y would be numeric vectors of equal length. Alternatively Y may be omitted and X may be a list with two components x and y, or a matrix with two columns.

Ignored by nnwhich.ppp and nnwhich.default.

k

Integer, or integer vector. The algorithm will compute the distance to the kth nearest neighbour.

by

Optional. A factor, which separates X into groups. The algorithm will find the nearest neighbour in each group.

method

String specifying which method of calculation to use. Values are "C" and "interpreted".

##### Details

For each point in the given point pattern, this function finds its nearest neighbour (the nearest other point of the pattern). By default it returns a vector giving, for each point, the index of the point's nearest neighbour. If k is specified, the algorithm finds each point's kth nearest neighbour.

The function nnwhich is generic, with method for point patterns (objects of class "ppp") and a default method which are described here, as well as a method for three-dimensional point patterns (objects of class "pp3", described in nnwhich.pp3.

The method nnwhich.ppp expects a single point pattern argument X. The default method expects that X and Y will determine the coordinates of a set of points. Typically X and Y would be numeric vectors of equal length. Alternatively Y may be omitted and X may be a list with two components named x and y, or a matrix or data frame with two columns.

The argument k may be a single integer, or an integer vector. If it is a vector, then the $$k$$th nearest neighbour distances are computed for each value of $$k$$ specified in the vector.

If the argument by is given, it should be a factor, of length equal to the number of points in X. This factor effectively partitions X into subsets, each subset associated with one of the levels of X. The algorithm will then find, for each point of X, the nearest neighbour in each subset.

If there are no points (if x has length zero) a numeric vector of length zero is returned. If there is only one point (if x has length 1), then the nearest neighbour is undefined, and a value of NA is returned. In general if the number of points is less than or equal to k, then a vector of NA's is returned.

The argument method is not normally used. It is retained only for checking the validity of the software. If method = "interpreted" then the distances are computed using interpreted R code only. If method="C" (the default) then C code is used. The C code is faster by two to three orders of magnitude and uses much less memory.

To evaluate the distance between a point and its nearest neighbour, use nndist.

To find the nearest neighbours from one point pattern to another point pattern, use nncross.

##### Value

Numeric vector or matrix giving, for each point, the index of its nearest neighbour (or kth nearest neighbour).

If k = 1 (the default), the return value is a numeric vector v giving the indices of the nearest neighbours (the nearest neighbout of the ith point is the jth point where j = v[i]).

If k is a single integer, then the return value is a numeric vector giving the indices of the kth nearest neighbours.

If k is a vector, then the return value is a matrix m such that m[i,j] is the index of the k[j]th nearest neighbour for the ith data point.

If the argument by is given, then the result is a data frame containing the indices described above, from each point of X, to the nearest point in each subset of X defined by the factor by.

##### Nearest neighbours of each type

If X is a multitype point pattern and by=marks(X), then the algorithm will find, for each point of X, the nearest neighbour of each type. See the Examples.

##### Warnings

A value of NA is returned if there is only one point in the point pattern.

##### Aliases
• nnwhich
• nnwhich.ppp
• nnwhich.default
##### Examples
# NOT RUN {
data(cells)
plot(cells)
m <- nnwhich(cells)
m2 <- nnwhich(cells, k=2)

b <- cells[m]
arrows(cells$x, cells$y, b$x, b$y, angle=15, length=0.15, col="red")

# find points which are the neighbour of their neighbour
self <- (m[m] == seq(m))
# plot them
A <- cells[self]
B <- cells[m[self]]
plot(cells)
segments(A$x, A$y, B$x, B$y)

# nearest neighbours of each type