clhs {clhs}

Conditioned Latin Hypercube Sampling

Description

Implementation of the conditioned Latin hypercube sampling, as published by Minasny and McBratney (2006) and the DLHS variant method (Minasny and McBratney, 2010). These methods propose to stratify sampling in presence of ancillary data. An extension of this method, which propose to associate a cost to each individual and take it into account during the optimisation process, is also proposed (Roudier et al., 2012).

Usage

clhs(
  x,
  size,
  must.include,
  can.include,
  cost,
  iter,
  use.cpp,
  temp,
  tdecrease,
  weights,
  eta,
  obj.limit,
  length.cycle,
  simple,
  progress,
  track,
  use.coords,
  ...
)

Arguments

x

A data.frame, SpatialPointsDataFrame, sf, or Raster object.

size

A non-negative integer giving the total number of items to select

must.include

A numeric vector giving the indices of the rows from x that must be included in the selected items. For the cost-constrained cLHS method, cost of these mandatory samples is set to 0. If NULL (default), all data are randomly chosen according to the classic cLHS method. If must.include is not NULL, argument size must include the total size of the final sample i.e. the size of mandatory samples given by must.include plus the size of the randomly chosen samples to pick.

can.include

A numeric vector giving indices of the rows from x that are allowed to be sampled from. The algorithm will use all of x as the reference distribution, but will only select samples from possible.sample. The option is only available in the C++ version; if use.cpp == FALSE, this parameter will be ignored.

cost

A character giving the name or an integer giving the index of the attribute in x that gives a cost that can be use to constrain the cLHS sampling. If NULL (default), the cost-constrained implementation is not used.

iter

A positive number, giving the number of iterations for the Metropolis-Hastings annealing process. Defaults to 10000.

use.cpp

TRUE or FALSE. If set to TRUE, annealing process uses C++ code. This is ~ 150 times faster than the R version, but is less stable and currently doesn't accept track or obj.limit parameters. Default to TRUE.

temp

The initial temperature at which the simulated annealing begins. Defaults to 1.

tdecrease

A number between 0 and 1, giving the rate at which temperature decreases in the simulated annealing process. Defaults to 0.95.

weights

A list a length 3, giving the relative weights for continuous data, categorical data, and correlation between variables. Defaults to list(numeric = 1, factor = 1, correlation = 1).

eta

Either a number equal 1 to perform a classic cLHS or a constrained cLHS or a matrix to perform a cLHS that samples more on the edge of the distibutions (DLHS, see details)

obj.limit

The minimal value at which the optimisation is stopped. Defaults to -Inf.

length.cycle

The duration (number of iterations) of the isotemperature steps. Defaults to 10.

simple

TRUE or FALSE. If set to TRUE, only the indices of the selected samples are returned, as a numeric vector. If set to FALSE, a cLHS_result object is returned (takes more memory but allows to make use of cLHS_results methods such as plot.cLHS_result).

progress

TRUE or FALSE, displays a progress bar.

track

A character giving the name or an integer giving the index of the attribute in x that gives a cost associated with each individual. However, this method will only track the cost - the sampling process will not be constrained by this attribute. If NULL (default), this option is not used.

use.coords

Logical, if TRUE the spatial coordinates of supported spatial objects (either a 'SpatialPointsDataFrame' object if using 'sp', or a 'sf' object if using 'sf') are included in the Latin hypercube calculations. Defaults to FALSE.

...

additional parameters passed to clhs

Details

For the DLHS method, the original paper defines parameter b as the importance of the edge of the distributions. A matrix eta (size N x K, where N is the size of the final sample and K the number of continuous variables) is defined, to compute the objective function of the algorithm, where each column equal the vector (b, 1, ..., 1, b) in order to give the edge of the distribution a probability b times higher to be sampled. In our function, instead of define the b parameter, users can defined their own eta matrix so that they can give more complex probability design of sampling each strata of the distribution instead of just be able to give more importance to both edges of the distribution.

Value

* If the simple option is set to TRUE (default behaviour): A numeric vector containing the indices of the selected samples is returned

* If the simple option is set to FALSE: An object of class cLHS_result, with the following elements:

index_samples

a vector giving the indices of the chosen samples.

sampled_data

the sampled data.frame.

obj

a vector giving the evolution of the objective function throughout the Metropolis-Hastings iterations.

cost

a vector giving the evolution of the cost function throughout the Metropolis-Hastings iterations (if available).

Author(s)

Pierre Roudier

References

*For the initial cLHS method:

Minasny, B. and McBratney, A.B. 2006. A conditioned Latin hypercube method for sampling in the presence of ancillary information. Computers and Geosciences, 32:1378-1388.

*For the DLHS method:

Minasny, B. and A. B. McBratney, A.B.. 2010. Conditioned Latin Hypercube Sampling for Calibrating Soil Sensor Data to Soil Properties. In: Proximal Soil Sensing, Progress in Soil Science, pages 111-119.

*For the cost-constrained implementation:

Roudier, P., Beaudette, D.E. and Hewitt, A.E. 2012. A conditioned Latin hypercube sampling algorithm incorporating operational constraints. In: Digital Soil Assessments and Beyond. Proceedings of the 5th Global Workshop on Digital Soil Mapping, Sydney, Australia.

See Also

plot.cLHS_result

Examples

df <- data.frame(
  a = runif(1000), 
  b = rnorm(1000), 
  c = sample(LETTERS[1:5], size = 1000, replace = TRUE)
)

# Returning the indices of the sampled points
res <- clhs(df, size = 50, progress = FALSE, simple = TRUE)
str(res)

# Returning a cLHS_result object for plotting using C++
res <- clhs(df, size = 50, use.cpp = TRUE, iter = 5000, progress = FALSE, simple = FALSE)
str(res)
plot(res)

# Method DLHS with a linear increase of the strata weight (i.e. probability to be sampled)
# from 1 for the middle starta to 3 for the edge of the distribution
linear_increase <- 1+(2/24)*0:24
eta <- matrix(c(rev(linear_increase), linear_increase), ncol = 2, nrow = 50)
set.seed(1)
res <- clhs(df, size = 50, iter = 100, eta = eta, progress = FALSE, simple = FALSE)
str(res)
plot(res)