Gmedian-package {Gmedian}

Geometric Median, k-Medians Clustering and Robust Median PCA

Description

The geometric median (also called spatial median or L1 median) is a robust multivariate indicator of central position. This library provides fast estimation procedures that can handle rapidly large samples of high dimensional data. Function Gmedian computes the geometric median of a numerical data set with averaged stochastic gradient algorithms, whereas GmedianCov computes the median covariation matrix, a useful indicator for robust PCA. Robust clustering, based on the geometric k-medians, can also be performed with the same type of recursive algorithm thanks to kGmedian. Less fast estimation procedures based on Weiszfeld's algorithm are also available : function Weiszfeld computes the geometric median whereas WeiszfeldCov computes the median covariation matrix. These procedures may be preferred for small and moderate sample sizes. Note that weighting statistical units (for example with survey sampling weights) is allowed.

Details

Package:	Gmedian
Type:	Package
Title:	Geometric Median, k-Medians Clustering and Robust Median PCA
Version:	1.2.7
Date:	2022-08-06
Author:	Herve Cardot
Maintainer:	Herve Cardot <[e-mail]>
Description:	Fast algorithms for robust estimation with large samples of multivariate observations. Estimation of the geometric median, robust k-Gmedian clustering, and robust PCA based on the Gmedian covariation matrix.
License:	GPL (>= 2)
Depends:	R (>= 3.0.0)
Imports:	Rcpp (>= 0.12.6), RSpectra, robustbase
LinkingTo:	Rcpp, RcppArmadillo, RSpectra
NeedsCompilation:	yes
Packaged:	2016-09-03 12:29:52 UTC; cardot
Repository:	CRAN
Date/Publication:	2016-09-05 16:35:51

Index of help topics:

Gmedian                 Gmedian
Gmedian-package         Geometric Median, k-Medians Clustering and
                        Robust Median PCA
GmedianCov              GmedianCov
Weiszfeld               Weiszfeld
WeiszfeldCov            WeiszfeldCov
kGmedian                kGmedian

Author(s)

Herve Cardot

Maintainer: Herve Cardot <[e-mail]>

References

Cardot, H., Cenac, P. and Zitt, P-A. (2013). Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. Bernoulli, 19, 18-43.

Cardot, H. and Godichon-Baggioni, A. (2017). Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Component7s Analysis. TEST, 26, 461-480.

Cardot, H., Cenac, P. and Monnez, J-M. (2012). A fast and recursive algorithm for clustering large datasets with k-medians. Computational Statistics and Data Analysis, 56, 1434-1449.

Lardin, P., Cardot, H. and Goga, C. (2014). Analyzing large datasets of functional data : a survey sampling point of view. Journal de la SFdS, 155, 70-94.

Vardi, Y. and Zhang, C.-H. (2000). The multivariate L1-median and associated data depth. Proc. Natl. Acad. Sci. USA, 97(4):1423-1426.