Compositional (version 1.2)

alfadist: The $\alpha$-distance

Description

This is the Euclidean distance after the $\alpha$-transformation has been applied.

Usage

alfadist(x, a)

Arguments

x

A matrix with the compositional data.

a

The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If $\alpha=0$ the isometric log-ratio transformation is applied and the solution exists in a closed form, since it the classical

Value

• A matrix including: The pairwise distances of all observations.

Details

The $\alpha$-transformation is applied to the compositional data first and then the Euclidean distance is calculated.

References

Tsagris M.T., Preston S. and Wood A.T.A. (2016). Improved classification for compositional data using the $\alpha$-transformation. Journal of Classification (to appear). http://arxiv.org/pdf/1506.04976v2.pdf Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. http://arxiv.org/pdf/1106.1451.pdf

See Also

alfa, alfainv, alfa.reg

Examples

library(MASS)
x <- fgl[1:20, 2:9]
alfadist(x, 0.1)
alfadist(x, 1)