# clusterset

0th

Percentile

##### Allard-Fraley Estimator of Cluster Feature

Detect high-density features in a spatial point pattern using the (unrestricted) Allard-Fraley estimator.

Keywords
spatial, classif
##### Usage
clusterset(X, what=c("marks", "domain"),
..., verbose=TRUE,
fast=FALSE,
exact=!fast)
##### Arguments
X
A dimensional spatial point pattern (object of class "ppp").
what
Character string or character vector specifying the type of result. See Details.
verbose
Logical value indicating whether to print progress reports.
fast
Logical. If FALSE (the default), the Dirichlet tile areas will be computed exactly using polygonal geometry, so that the optimal choice of tiles will be computed exactly. If TRUE, the Dirichlet tile areas will be
exact
Logical. If TRUE, the Allard-Fraley estimator of the domain will be computed exactly using polygonal geometry. If FALSE, the Allard-Fraley estimator of the domain will be approximated by a binary pixel mask. The d
...
Optional arguments passed to as.mask to control the pixel resolution if exact=FALSE.
##### Details

Allard and Fraley (1997) developed a technique for recognising features of high density in a spatial point pattern in the presence of random clutter.

This algorithm computes the unrestricted Allard-Fraley estimator. The Dirichlet (Voronoi) tessellation of the point pattern X is computed. The smallest m Dirichlet cells are selected, where the number m is determined by a maximum likelihood criterion.

• Iffast=FALSE(the default), the areas of the tiles of the Dirichlet tessellation will be computed exactly using polygonal geometry. This ensures that the optimal selection of tiles is computed exactly.
• Iffast=TRUE, the Dirichlet tile areas will be approximated by counting pixels. This is faster, and is usually correct (depending on the pixel resolution, which is controlled by the arguments...).

The type of result depends on the character vector what.

• Ifwhat="marks"the result is the point patternXwith a vector of marks labelling each point with a valueyesornodepending on whether the corresponding Dirichlet cell is selected by the Allard-Fraley estimator. In other words each point ofXis labelled as either a cluster point or a non-cluster point.
• Ifwhat="domain", the result is the Allard-Fraley estimator of the cluster feature set, which is the union of all the selected Dirichlet cells, represented as a window (object of class"owin").
• Ifwhat=c("marks", "domain")the result is a list containing both of the results described above.

Computation of the Allard-Fraley set estimator depends on the argument exact.

• Ifexact=TRUE(the default), the Allard-Fraley set estimator will be computed exactly using polygonal geometry. The result is a polygonal window.
• Ifexact=FALSE, the Allard-Fraley set estimator will be approximated by a binary pixel mask. This is faster than the exact computation. The result is a binary mask.

##### Value

• If what="marks", a multitype point pattern (object of class "ppp").

If what="domain", a window (object of class "owin").

If what=c("marks", "domain") (the default), a list consisting of a multitype point pattern and a window.

##### References

Allard, D. and Fraley, C. (1997) Nonparametric maximum likelihood estimation of features in spatial point processes using Voronoi tessellation. Journal of the American Statistical Association 92, 1485--1493.

nnclean, sharpen

• clusterset
##### Examples
opa <- par(mfrow=c(1,2))
W <- grow.rectangle(as.rectangle(letterR), 1)
X <- superimpose(runifpoint(300, letterR),
runifpoint(50, W), W=W)
plot(W, main="clusterset(X, 'm')")
plot(clusterset(X, "marks", fast=TRUE), add=TRUE, chars=c(1, 3), cols=1:2)
par(opa)