sharpen
Data Sharpening of Point Pattern
Performs Choi-Hall data sharpening of a spatial point pattern.
- Keywords
- spatial, nonparametric
Usage
sharpen(X, ...)
## S3 method for class 'ppp':
sharpen(X, sigma=NULL, ..., varcov=NULL,
edgecorrect=FALSE)
Arguments
- X
- A marked point pattern (object of class
"ppp"
). - sigma
- Standard deviation of isotropic Gaussian smoothing kernel.
- varcov
- Variance-covariance matrix of anisotropic Gaussian kernel.
Incompatible with
sigma
. - edgecorrect
- Logical value indicating whether to apply edge effect bias correction.
- ...
- Arguments passed to
density.ppp
to control the pixel resolution of the result.
Details
Choi and Hall (2001) proposed a procedure for data sharpening of spatial point patterns. This procedure is appropriate for earthquake epicentres and other point patterns which are believed to exhibit strong concentrations of points along a curve. Data sharpening causes such points to concentrate more tightly along the curve. If the original data points are $X_1, \ldots, X_n$ then the sharpened points are $$\hat X_i = \frac{\sum_j X_j k(X_j-X_i)}{\sum_j k(X_j - X_i)}$$ where $k$ is a smoothing kernel in two dimensions. Thus, the new point $\hat X_i$ is a vector average of the nearby points $X[j]$.
The function sharpen
is generic. It currently has only one
method, for two-dimensional point patterns (objects of class
"ppp"
).
If sigma
is given, the smoothing kernel is the
isotropic two-dimensional Gaussian density with standard deviation
sigma
in each axis. If varcov
is given, the smoothing
kernel is the Gaussian density with variance-covariance matrix
varcov
.
The data sharpening procedure tends to cause the point pattern
to contract away from the boundary of the window. That is,
points X_i
{X[i]} that lie `quite close to the edge of the window
of the point pattern tend to be displaced inward.
If edgecorrect=TRUE
then the algorithm is modified to
correct this vector bias.
Value
- A point pattern (object of class
"ppp"
) in the same window as the original patternX
, and with the same marks asX
.
References
Choi, E. and Hall, P. (2001) Nonparametric analysis of earthquake point-process data. In M. de Gunst, C. Klaassen and A. van der Vaart (eds.) State of the art in probability and statistics: Festschrift for Willem R. van Zwet, Institute of Mathematical Statistics, Beachwood, Ohio. Pages 324--344.
See Also
Examples
data(shapley)
X <- unmark(shapley)
if(!(interactive())) X <- rthin(X, 0.05)
Y <- sharpen(X, sigma=0.5)