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)X |
A dimensional spatial point pattern (object of class
|
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 |
exact |
Logical. If |
... |
Optional arguments passed to |
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.
If 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.
If 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.
If what="marks" the result is the point pattern X
with a vector of marks labelling each point with a value yes or
no depending on whether the corresponding Dirichlet cell is
selected by the Allard-Fraley estimator. In other words each point of
X is labelled as either a cluster point or a non-cluster point.
If 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
"owin").
If 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
the argument exact.
If exact=TRUE (the default), the Allard-Fraley set estimator
will be computed exactly using polygonal geometry.
The result is a polygonal window.
If 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.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.