Multivariate L1 Median

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Description

Computes the multivariate L1 median (also called spatial median) of a data matrix.

Usage

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l1median(X, MaxStep = 200, ItTol = 10^-8, trace = 0, m.init = .colMedians (X))

Arguments

X

A matrix containing the values whose multivariate L1 median is to be computed.

MaxStep

The maximum number of iterations.

ItTol

Tolerance for convergence of the algorithm.

trace

The tracing level.

m.init

An initial estimate.

Value

returns the vector of the coordinates of the L1 median.

Author(s)

Heinrich Fritz, Peter Filzmoser <P.Filzmoser@tuwien.ac.at>

References

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

See Also

median

Examples

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  l1median(rnorm(100), trace = -1) # this returns the median of the sample

  # multivariate data with outliers
  library(mvtnorm)
  x <- rbind(rmvnorm(200, rep(0, 4), diag(c(1, 1, 2, 2))), 
             rmvnorm( 50, rep(3, 4), diag(rep(2, 4))))
  l1median(x, trace = -1)
  # compare with coordinate-wise median:
  apply(x,2,median)