Allard-Fraley Estimator of Cluster Feature
Detect high-density features in a spatial point pattern using the (unrestricted) Allard-Fraley estimator.
clusterset(X, what=c("marks", "domain"), ..., verbose=TRUE, fast=FALSE, exact=!fast)
- A dimensional spatial point pattern (object of class
- Character string or character vector specifying the type of result. See Details.
- Logical value indicating whether to print progress reports.
- 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
- 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.maskto control the pixel resolution if
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
computed. The smallest
m Dirichlet cells are selected,
where the number
m is determined by a maximum likelihood
fast=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.
fast=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="marks"the result is the point pattern
Xwith a vector of marks labelling each point with a value
nodepending on whether the corresponding Dirichlet cell is selected by the Allard-Fraley estimator. In other words each point of
Xis labelled as either a cluster point or a non-cluster point.
what="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
what=c("marks", "domain")the result is a list containing both of the results described above.
Computation of the Allard-Fraley set estimator depends on
exact=TRUE(the default), the Allard-Fraley set estimator will be computed exactly using polygonal geometry. The result is a polygonal window.
exact=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.
what="marks", a multitype point pattern (object of class
what="domain", a window (object of class
what=c("marks", "domain")(the default), a list consisting of a multitype point pattern and a window.
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.
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) plot(letterR, add=TRUE) plot(W, main="clusterset(X, 'd')") plot(clusterset(X, "domain", exact=FALSE), add=TRUE) plot(letterR, add=TRUE) par(opa)