R: Aitchison distance

aDist {robCompositions} | R Documentation

## 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)

[Package robCompositions version 2.3.1 Index]