robCompositions (version 2.4.1)

aDist: Aitchison distance

Description

Computes the Aitchison distance between two observations, between two data sets or within observations of one data set.

Usage

aDist(x, y = NULL)
iprod(x, y)

Value

The Aitchison distance between two compositions or between two data sets, or a distance matrix in case codey is not supplied.

Arguments

x

a vector, matrix or data.frame

y

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

Author

Matthias Templ, Bernhard Meindl

Details

This distance measure accounts for the relative scale property of compositional data. It measures the distance between two compositions if x and y are vectors. It evaluates the 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 computes a n times n distance matrix (with n the number of observations/compositions) if only x is provided.

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

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

pivotCoord

Examples

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

## Aitchison distance of x:
aDist(x)

## Example of distances between matrices:
## set some missing values:
x[1,3] <- x[3,5] <- x[2,4] <- x[5,3] <- x[8,3] <- NA

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

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

data("expenditures") 
aDist(expenditures)  
x <- expenditures[, 1]
y <- expenditures[, 2]
aDist(x, y)
aDist(expenditures, expenditures)