mrfDepth (version 1.0.17)

dprojmedian: Location estimates based on directional projection depth

Description

Computes a directional projection depth based location estimate of a \(p\)-dimensional dataset x.

Usage

dprojmedian(x, dprojection.depths = NULL, options = NULL)

Value

A list with component:

max

The observation of x with maximal directional projection depth. If multiple points have maximum depth, their center of gravity is returned.

Arguments

x

An \(n\) by \(p\) data matrix with observations in the rows and variables in the columns.

dprojection.depths

Vector containing the directional projection depth of the observations in x.

options

A list of options to pass to the dprojdepth routine. See dprojdepth for more details.

Author

J. Raymaekers

Details

The algorithm depends on the function dprojdepth to compute the directional projection depth of the observations in x. If these depth values have already been computed they can be passed as an optional argument to save computing time. If not, directional projection depth values will be computed and the user can pass a list with options to the dprojdepth function.

It is first checked whether the data lie in a subspace of dimension smaller than \(p\). If so, a warning is given, as well as the dimension of the subspace and a direction which is orthogonal to it.

References

Rousseeuw P.J., Raymaekers J., Hubert M. (2018). A measure of directional outlyingness with applications to image data and video. Journal of Computational and Graphical Statistics, 27, 345--359.

See Also

dirOutl, dprojdepth, adjOutl, outlyingness

Examples

# Compute a location estimate of a two-dimensional dataset.
data(bloodfat)
result <- dprojmedian(x = bloodfat)
plot(bloodfat, pch = 16)
points(result$max, col = "red", pch = 18, cex = 1.5)

# Options for the underlying dprojdepth routine may be passed 
# using the options argument. 
result <- dprojmedian(x = bloodfat, options = list(type = "Rotation", ndir = 100))
plot(bloodfat, pch = 16)
points(result$max, col = "red", pch = 18, cex = 1.5)

# One may also compute the depth values of the observations in the data
# separately. This avoids having to recompute them when conmputing the median. 
depth.result <- dprojdepth(x = bloodfat)
result <- dprojmedian(x = bloodfat, dprojection.depths = depth.result$depthX)