robCompositions (version 2.0.0)

aDist: Aitchison distance

Description

Computes the Aitchison distance between two observations or between two data sets.

Usage

aDist(x, y)

Arguments

x

a vector, matrix or data.frame

y

a vector, matrix or data.frame with equal dimension as x

Value

The Aitchison distance between two compositions or between two data sets.

Details

This distance measure accounts for the relative scale property of the Aitchison distance. It measures the distance between two compositions if x and y are vectors and evaluate sum of the distances between x and y for each row of x and y if x and y are matrices or data frames.

It is to compare two matrices.

The underlying code is written in C and allows a fast computation also for large data sets.

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman and Hall Ltd., London (UK). 416p.

Aitchison, J. and Barcelo-Vidal, C. and Martin-Fernandez, J.A. and Pawlowsky-Glahn, V. (2000) Logratio analysis and compositional distance. Mathematical Geology, 32, 271-275.

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.

See Also

isomLR

Examples

data(expenditures)
x <- xOrig <- expenditures
## Aitchison distance between the first 2 observations:
aDist(x[,1], x[,2])

## set some missing values:
x[1,3] <- x[3,5] <- x[2,4] <- x[5,3] <- x[8,3] <- NA

## impute them:
xImp <- impCoda(x, method="ltsReg")$xImp

## calculate the relative Aitchsion distance between xOrig and xImp:
aDist(xOrig, xImp)