mediancenter {fastmatrix}

Mediancenter

Description

It calculates the mediancenter (or geometric median) of multivariate data.

Usage

mediancenter(x)

Arguments

x

a matrix or data frame. As usual, rows are observations and columns are variables.

Details

The mediancenter for a sample of multivariate observations is computed using a steepest descend method combined with bisection. The mediancenter invariant to rotations of axes and is useful as a multivariate generalization of the median of univariate sample.

Value

A list containing the following named components:

median

an estimate for the mediancenter of the data.

iter

the number of iterations performed, it is negative if a degenerate solution is found.

References

Gower, J.C. (1974). Algorithm AS 78: The mediancentre. Applied Statistics 23, 466-470.

See Also

cov.wt, median.

Examples

x <- cbind(1:10, c(1:3, 8:5, 8:10))
z <- mediancenter(x)$median # degenerate solution
xbar <- colMeans(x)
plot(x, xlab = "", ylab = "")
points(x = xbar[1], y = xbar[2], pch = 16, col = "red")
points(x = z[1], y = z[2], pch = 3, col = "blue", lwd = 2)