spsann (version 1.0.1)

spJitterFinite: Random perturbation of spatial points

Description

Perturb the coordinates of spatial points (jittering).

Usage

spJitterFinite(points, candi, x.max, x.min, y.max, y.min, which.point)

Arguments

points

Integer value, integer vector, data frame or matrix. If points is an integer value, it defines the number of points that should be randomly sampled from candi to form the starting system configuration. If points is a

candi

Data frame or matrix with the candidate locations for the perturbed points. candi must have two columns in the following order: [, "x"] the projected x-coordinates, and [, "y"] the projected y-coordinates.

x.max,x.min,y.max,y.min

Numeric value. The minimum and maximum quantity of random noise to be added to the projected x- and y-coordinates. The minimum quantity should be equal to, at least, the minimum distance between two neighbouring candidate locations. The units are the same

which.point

Integer values defining which point should be perturbed.

Value

• A matrix with the jittered projected coordinates of the points.

Jittering methods

There are two ways of jittering the coordinates. They differ on how the set of candidate locations is defined. The first method uses an infinite set of candidate locations, that is, any point in the spatial domain can be selected as the new location of a perturbed point. All that this method needs is a polygon indicating the boundary of the spatial domain. This method is not implemented in the spsann package (yet) because it is computationally demanding: every time a point is jittered, it is necessary to check if it is inside the spatial domain.

The second method consists of using a finite set of candidate locations for the perturbed points. A finite set of candidate locations is created by discretizing the spatial domain, that is, creating a fine grid of points that serve as candidate locations for the perturbed points. This is the only method currently implemented in the spsann package because it is one of the least computationally demanding.

Using a finite set of candidate locations has one important inconvenience. When a point is selected to be jittered, it may be that the new location already is occupied by another point. If this happens, another location is iteratively sought for as many times as there are points in points. Because the more points there are in points, the more likely it is that the new location already is occupied by another point. If a solution is not found, the point selected to be jittered point is kept in its original location.

A more elegant method can be defined using a finite set of candidate locations coupled with a form of two-stage random sampling as implemented in spsample. Because the candidate locations are placed on a finite regular grid, they can be seen as being the centre nodes of a finite set of grid cells (or pixels of a raster image). In the first stage, one of the grid cells is selected with replacement, i.e. independently of already being occupied by another sample point. The new location for the point chosen to be jittered is selected within that grid cell by simple random sampling. This method guarantees that any location in the spatial domain can be a candidate location. It also discards the need to check if the new location already is occupied by another point. This method is not implemented (yet) in the spsann package.

Distance between two points

The distance between two points is computed as the Euclidean distance between them. This computation assumes that the optimization is operating in the two-dimensional Euclidean space, i.e. the coordinates of the sample points and candidate locations should not be provided as latitude/longitude. Package spsann has no mechanism to check if the coordinates are projected, and the user is responsible for making sure that this requirement is attained.

concept

jitter perturb

References

Edzer Pebesma, Jon Skoien with contributions from Olivier Baume, A. Chorti, D.T. Hristopulos, S.J. Melles and G. Spiliopoulos (2013). intamapInteractive: procedures for automated interpolation - methods only to be used interactively, not included in intamap package. R package version 1.1-10.

van Groenigen, J.-W. Constrained optimization of spatial sampling: a geostatistical approach. Wageningen: Wageningen University, p. 148, 1999.

See Also

ssaOptim, zerodist, jitter, jitter2d.

Examples

require(sp)
data(meuse.grid)
meuse.grid <- as.matrix(meuse.grid[, 1:2])
meuse.grid <- matrix(cbind(1:dim(meuse.grid)[1], meuse.grid), ncol = 3)
pts1 <- sample(c(1:dim(meuse.grid)[1]), 155)
pts2 <- meuse.grid[pts1, ]
pts3 <- spJitterFinite(points = pts2, candi = meuse.grid, x.min = 40,
                      x.max = 100, y.min = 40, y.max = 100, which.point = 10)
plot(meuse.grid[, 2:3], asp = 1, pch = 15, col = "gray")
points(pts2[, 2:3], col = "red", cex = 0.5)
points(pts3[, 2:3], pch = 19, col = "blue", cex = 0.5)

# Cluster of points
pts1 <- c(1:55)
pts2 <- meuse.grid[pts1, ]
pts3 <- spJitterFinite(points = pts2, candi = meuse.grid, x.min = 40,
                      x.max = 80, y.min = 40, y.max = 80, which.point = 1)
plot(meuse.grid[, 2:3], asp = 1, pch = 15, col = "gray")
points(pts2[, 2:3], col = "red", cex = 0.5)
points(pts3[, 2:3], pch = 19, col = "blue", cex = 0.5)