optimFREQ  R Documentation 
Optimize a sample configuration for spatial trend identification and estimation. A criterion is defined so that the sample reproduces the frequency marginal distribution of the covariates (FREQ).
optimFREQ(
points,
candi,
covars,
strata.type = "area",
use.coords = FALSE,
schedule,
plotit = FALSE,
track = FALSE,
boundary,
progress = "txt",
verbose = FALSE
)
objFREQ(points, candi, covars, strata.type = "area", use.coords = FALSE)
optimDIST(
points,
candi,
covars,
strata.type = "area",
use.coords = FALSE,
schedule,
plotit = FALSE,
track = FALSE,
boundary,
progress = "txt",
verbose = FALSE
)
objDIST(points, candi, covars, strata.type = "area", use.coords = FALSE)
points 
Integer value, integer vector, data frame (or matrix), or list. The number of sampling points (sample size) or the starting sample configuration. Four options are available:
Most users will want to set an integer value simply specifying the required sample size. Using an integer vector or data frame (or matrix) will generally be helpful to users willing to evaluate starting sample configurations, test strategies to speed up the optimization, and finetune or thin an existing sample configuration. Users interested in augmenting a possibly existing realworld sample configuration or finetuning only a subset of the existing sampling points will want to use a list. 
candi 
Data frame (or matrix). The Cartesian x and ycoordinates (in this order) of the
cell centres of a spatially exhaustive, rectangular grid covering the entire spatial sampling
domain. The spatial sampling domain can be contiguous or composed of disjoint areas and contain
holes and islands. 
covars 
Data frame or matrix with the spatially exhaustive covariates in the columns. 
strata.type 
(Optional) Character value setting the type of stratification that should be used to create the marginal sampling strata (or factor levels) for the numerical covariates. Two options are available:
The first option ( 
use.coords 
(Optional) Logical value. Should the projected spatial x and ycoordinates
be used as spatially exhaustive covariates? Defaults to 
schedule 
List with named subarguments setting the control parameters of the annealing
schedule. See 
plotit 
(Optional) Logical for plotting the evolution of the optimization. Plot updates
occur at each ten (10) spatial jitters. Defaults to

track 
(Optional) Logical value. Should the evolution of the energy state be recorded and
returned along with the result? If 
boundary 
(Optional) An object of class SpatialPolygons (see sp::SpatialPolygons()) with
the outer and inner limits of the spatial sampling domain (see 
progress 
(Optional) Type of progress bar that should be used, with options 
verbose 
(Optional) Logical for printing messages about the progress of the optimization.
Defaults to 
There are multiple mechanism to generate a new sample configuration out of an existing one. The main step consists of randomly perturbing the coordinates of a single sample, a process known as ‘jittering’. These mechanisms can be classified based on how the set of candidate locations for the samples is defined. For example, one could use an infinite set of candidate locations, that is, any location in the spatial domain can be selected as a new sample location after a sample is jittered. All that is needed is a polygon indicating the boundary of the spatial domain. This method is more computationally demanding because every time an existing sample is jittered, it is necessary to check if the new sample location falls in spatial domain.
Another approach consists of using a finite set of candidate locations for the samples. A finite set of candidate locations is created by discretising the spatial domain, that is, creating a fine (regular) grid of points that serve as candidate locations for the jittered sample. This is a less computationally demanding jittering method because, by definition, the new sample location will always fall in the spatial domain.
Using a finite set of candidate locations has two important inconveniences. First, not all locations in the spatial domain can be selected as the new location for a jittered sample. Second, when a sample is jittered, it may be that the new location already is occupied by another sample. If this happens, another location has to be iteratively sought for, say, as many times as the size of the sample configuration. In general, the larger the size of the sample configuration, the more likely it is that the new location already is occupied by another sample. If a solution is not found in a reasonable time, the the sample selected to be jittered is kept in its original location. Such a procedure clearly is suboptimal.
spsann uses a more elegant method which is based on using a finite set of candidate locations
coupled with a form of twostage random sampling as implemented in spcosa::spsample()
.
Because the candidate locations are placed on a finite regular grid, they can be taken as 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. The new location for the sample chosen to be jittered is selected
within that “grid cell” by simple random sampling. This method guarantees that virtually
any location in the spatial domain can be selected. It also discards the need to check if the new
location already is occupied by another sample, speeding up the computations when compared to the
first two approaches.
Reproducing the frequency marginal distribution of the numeric covariates depends upon the definition of marginal sampling strata. These marginal sampling strata are also used to define the factor levels of all numeric covariates that are passed together with factor covariates. Two types of marginal sampling strata can be used: equalarea and equalrange.
Equalarea marginal sampling strata are defined using the sample quantiles estimated with
stats::quantile()
using a discontinuous function(type = 3
). Using a discontinuous function
avoids creating breakpoints that do not occur in the population of existing covariate values.
Depending on the level of discretization of the covariate values, stats::quantile()
produces
repeated breakpoints. A breakpoint will be repeated if that value has a relatively high frequency
in the population of covariate values. The number of repeated breakpoints increases with the
number of marginal sampling strata. Repeated breakpoints result in empty marginal sampling
strata. To avoid this, only the unique breakpoints are used.
Equalrange marginal sampling strata are defined by breaking the range of covariate values into pieces of equal size. Depending on the level of discretization of the covariate values, this method creates breakpoints that do not occur in the population of existing covariate values. Such breakpoints are replaced with the nearest existing covariate value identified using Euclidean distances.
Like the equalarea method, the equalrange method can produce empty marginal sampling strata. The solution used here is to merge any empty marginal sampling strata with the closest nonempty marginal sampling strata. This is identified using Euclidean distances as well.
The approaches used to define the marginal sampling strata result in each numeric covariate having a different number of marginal sampling strata, some of them with different area/size. Because the goal is to have a sample that reproduces the frequency marginal distribution of the covariate, each marginal sampling strata will have a different number of sample points. The wanted distribution of the number of sample points per marginal strata is estimated empirically as the proportion of points in the population of existing covariate values that fall in each marginal sampling strata.
optimFREQ
(optimDIST
) returns an object of class OptimizedSampleConfiguration
: the
optimized sample configuration with details about the optimization.
objFREQ
(objDIST
) returns a numeric value: the energy state of the sample configuration –
the objective function value.
spsann always computes the distance between two locations (points) as the Euclidean distance between them. This computation requires the optimization to operate in the twodimensional Euclidean space, i.e. the coordinates of the sample, candidate and evaluation locations must be Cartesian coordinates, generally in metres or kilometres. spsann has no mechanism to check if the coordinates are Cartesian: you are the sole responsible for making sure that this requirement is attained.
Alessandro SamuelRosa alessandrosamuelrosa@gmail.com
Hyndman, R. J.; Fan, Y. Sample quantiles in statistical packages. The American Statistician, v. 50, p. 361365, 1996.
Everitt, B. S. The Cambridge dictionary of statistics. Cambridge: Cambridge University Press, p. 432, 2006.
optimACDC()
#####################################################################
# NOTE: The settings below are unlikely to meet your needs. #
#####################################################################
if (interactive() & require(sp)) {
data(meuse.grid, package = "sp")
schedule < scheduleSPSANN(
initial.temperature = 1, chains = 1,
x.max = 1540, y.max = 2060, x.min = 0,
y.min = 0, cellsize = 40)
set.seed(2001)
res < optimDIST(points = 10, candi = meuse.grid[, 1:2],
covars = meuse.grid[, 5], use.coords = TRUE, schedule = schedule)
objSPSANN(res) 
objDIST(points = res, candi = meuse.grid[, 1:2],
covars = meuse.grid[, 5],
use.coords = TRUE)
}
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