Gmedian-package: Geometric Median, k-Medians Clustering and Robust Median PCA

In Gmedian: Geometric Median, k-Medians Clustering and Robust Median PCA

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

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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.

Gmedian documentation built on June 8, 2022, 5:07 p.m.