Geometric median of a composition in clr coordinates

clr(x)_j = log(x_j / (prod_l x_l)^(1/D)); the spatial median of the clr scores minimises sum_i ||clr(x_i) - m|| and is found by the Weiszfeld iteration m <- sum_i y_i/d_i / sum_i 1/d_i. The estimate is mapped back to the simplex by the inverse clr.

Usage

Clrmedian(X, steps = 100, eps = 1e-12)

Arguments

X

Strictly positive compositions, one per row.

steps

Fixed Weiszfeld iteration count.

eps

Distances below this are treated as coincident.

Value

List with median, clrmed, objective, clrmean, n, D, steps.

References

Filzmoser and Hron (2008), Mathematical Geosciences 40(3), 233-248; clr is Aitchison's transform and the spatial median is Weiszfeld's (1937).

Examples

M <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2)
Clrmedian(M)
#> $median
#> [1] 0.1365659 0.3345167 0.5289174
#> 
#> $clrmed
#> [1] -0.7499683  0.1459115  0.6040568
#> 
#> $objective
#> [1] 0.3814209
#> 
#> $clrmean
#> [1] -0.7499683  0.1459115  0.6040568
#> 
#> $n
#> [1] 2
#> 
#> $D
#> [1] 3
#> 
#> $steps
#> [1] 100
#> 
#> $method
#> [1] "Spatial median in clr coordinates (Weiszfeld iteration)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"