Yamm-package: Multivariate Methods Based on Projections and Related...

In Yamm: Multivariate Methods Based on Projections and Related Concepts

Multivariate Methods Based on Projections and Related Concepts

Description

This package provides functions for computing the projection median. PmedTrapz approximates the projection median by the trapezoidal rule, which is only valid for the two- and three-dimensional cases, while PmedMCInt use Monte Carlo approximation, and it is valid for any multivariate median. yamm provides another method to compute the projection median based on an optimiser technique. This package also provides functions for plotting different multivariate medians, such as the Spatial, Component-wise, Tukey's, etc., for randomly generated data sets in both the two-dimensional and three-dimensional cases. In addition, this package also allows users to produce the two-dimensional and three-dimensional quantile plots with function muqie and muqie3D respectively.

Details

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Author(s)

Fan Chen [aut], Guy Nason [aut, cre]

Maintainer: Guy Nason <[e-mail]>

References

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

Chen, F. and Nason, Guy P. (2020) A new method for computing the projection medi an, its influence curve and techniques for the production of projected quantile plots. PLOS One, doi: 10.1371/journal.pone.0229845

Croux, C., Filzmoser, P., and Oliveira, M., (2007). Algorithms for Projection-Pursuit Robust Principal Component Analysis, Chemometrics and Intelligent Laboratory Systems, 87, 218-225.

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

Rousseeuw, P.J. and Ruts, I. (1996), Algorithm AS 307: Bivariate location depth, Appl. Stat.-J. Roy. St. C, 45, 516-526.

Rousseeuw, P.J. and Ruts, I. (1998), Constructing the bivariate Tukey median, Stat. Sinica, 8, 828-839.

Rousseeuw, P.J., Ruts, I., and Tukey, J.W. (1999), The Bagplot: A Bivariate Boxplot, The Am. Stat., 53, 382-387.

Struyf, A. and Rousseeuw, P.J. (2000), High-dimensional computation of the deepest location, Comput. Statist. Data Anal., 34, 415-436.

See Also

yamm, PmedTrapz, PmedMCInt,

Examples

# 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 = 30000)
# [1]  4.3369501 -0.1578591
#
#
# Projection median approximated by the trapezoidal rule.
PmedTrapz(clusters2d,no.subinterval=180)
# [1]  4.1556553 -0.3566614
#
#
# Yamm.
set.seed(5)
yamm(clusters2d,nprojs = 2500,reltol=1e-3,doabs=1,full.results=FALSE)
# [1]  4.3871582 -0.1070497
#
#
# Plot 2-D medians
# Remove the outliers of the dataset.
cluster_without_outlier <- clusters2d[c(1:101),]
myxvec <- c(min(cluster_without_outlier[,1]), 
          max(cluster_without_outlier[,1]))
myyvec <- c(min(cluster_without_outlier[,2]), 
          max(cluster_without_outlier[,2]))
#
# Plot the figure.
set.seed(5)
Plot2dMedian(clusters2d, myxvec, myyvec, yamm.nprojs = 2000, 
             PmedMCInt.nprojs = 20000, no.subinterval = 36, 
             opt.method = "BFGS", xlab = "Component1",
             ylab = "Component2")

Yamm documentation built on May 20, 2022, 5:06 p.m.