robCompositions (version 2.0.0)

isomLR: Isometric log-ratio transformation

Description

An isometric log-ratio transformation (ilr1) and it's inverse transformation with a special choice of the balances

Usage

isomLR(x, fast = FALSE)
isomLRinv(x)

Arguments

x

object of class data.frame or matrix. Positive values only for isomLR().

fast

if TRUE, it is approx. 10 times faster but numerical problems in case of high-dimensional data may occur.

Value

The transformed data.

Details

The isomLR transformation moves D-part compositional data from the simplex into a (D-1)-dimensional real space isometrically. From our choice of the balances (ilr1), all the relative information of the part $x_1$ from the remaining parts is separated. It is useful for estimating missing values in $x_1$ by regression of the remaining variables.

References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300. \

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing values for compositional data using classical and robust methods Computational Statistics and Data Analysis, vol 54 (12), pages 3095-3107.

Examples

require(MASS)
Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)
z <- isomLRinv(mvrnorm(100, mu=c(0,2), Sigma=Sigma))

data(expenditures)
isomLR(expenditures)

x <- exp(mvrnorm(2000, mu=rep(1,10), diag(10)))
system.time(isomLR(x))
system.time(isomLR(x, fast=TRUE))