Yamm (version 1.3.2)

PmedMCInt: Projection Median Approximated by Monte Carlo Integration

Description

This function approximates the projection median using Monte Carlo integration, which can be used for any dimensions. PmedMCInt is implemented internally using C code CPmedMCInt and hence is much faster than coding with R only.

Usage

PmedMCInt(x, nprojs = 20000)

Arguments

x

The data as a matrix or data frame, with each row being viewed as one multivariate observation.

nprojs

The number of projections when using the Monte Carlo method to approximate the integration. The default value is 20000, since PmedMCInt requires large a number of projections to ensure the accuracy. More projections may increase the accuracy, as well as the running time.

Value

A vector of the projection median for \(n\)-dimensional data.

Details

The projection median was introduced by Durocher and Kirkpatrick (2009) and generalised by Basu, Bhattacharya and Talukdar (2012). PmedMCInt produces the projection median using Monte Carlo approximation, which is valid in any multi-dimensional data. However, a large number of projections is sometimes required to ensure accuracy, which will also increase the running time. In this case, PmedTrapz is preferred for the two- or three-dimensional data, which is fast and accurate in general. In higher dimensions, yamm is another alternative for computing the projection median.

References

Durocher, S. and Kirkpatrick, D. (2009), The projection median of a set of points, Computational Geometry,42, 364-375.

Basu, R., Bhattacharya, B.B., and Talukdar, T. (2012) The projection median of a set of points in Rd CCCG., 47, 329-346. 10.1007/s00454-011-9380-6

See Also

PmedTrapz, yamm

Examples

# NOT RUN {
# Load a 2-dimensional data set
data(clusters2d)
#
# Set seed for reproduction.
set.seed(5)
#
# Projection median approximated by Monte Carlo Integration.
PmedMCInt(clusters2d, nprojs = 50000)
# [1]  4.3246488 -0.1535201
#
#
# Load a 6-dimensional data set
data(beetle)
#
set.seed(5)
PmedMCInt(beetle,nprojs = 150000)
# [1] 179.92439 125.16939  50.01176 136.55460  13.22277  95.04224
# }