aDist: Aitchison distance

In robCompositions: Compositional Data Analysis

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)

Arguments

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

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.

Value

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

Author(s)

Matthias Templ, Bernhard Meindl

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)

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.