compositions (version 0.9-11)

apt: Additive planar transform

Description

Compute the additive planar transform of a (dataset of) compositions and its inverse.

Usage

apt( x )
          apt.inv( z )

Arguments

x

a composition or a matrix of compositions, not necessarily closed

z

the apt-transform of a composition or a matrix of alr-transforms of compositions

Value

• apt gives the centered planar transform, apt.inv gives closed compositions with the given apt-transforms

Details

The apt-transform maps a composition in the D-part real-simplex linearly to a D-1 dimensional euclidian vector. Although the transformation does not reach the whole $R^{D-1}$, resulting covariance matrices are typically of full rank. The data can then be analysed in this transformation by all classical multivariate analysis tools not relying on distances. See cpt and ipt for alternatives. The interpretation of the results is easy since the relation to the first D-1 original variables is preserved. The additive planar transform is given by $$apt(x)_i := clo(x)_i, i=1,\ldots,D-1$$

See Also

alr,cpt,ipt

Examples

(tmp <- apt(c(1,2,3)))
apt.inv(tmp)
apt.inv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(apt(cdata))