Compositional (version 5.5)

The alpha-distance: The $\alpha$-distance

Description

This is the Euclidean (or Manhattan) distance after the $\alpha$-transformation has been applied.

Usage

alfadist(x, a, type = "euclidean", square = FALSE)
alfadista(xnew, x, a, type = "euclidean", square = FALSE)

Arguments

xnew

A matrix or a vector with new compositional data.

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.

type

Which type distance do you want to calculate after the $\alpha$-transformation, "euclidean", or "manhattan".

square

In the case of the Euclidean distance, you can choose to return the squared distance by setting this TRUE.

Value

For "alfadist" a matrix including the pairwise distances of all observations or the distances between xnew and x. For "alfadista" a matrix including the pairwise distances of all observations or the distances between xnew and x.

Details

The $\alpha$-transformation is applied to the compositional data first and then the Euclidean or the Manhattan 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. 33(2):243--261. https://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. https://arxiv.org/pdf/1106.1451.pdf

See Also

alfa, alfainv, alfa.reg, esov

Examples

# NOT RUN {
library(MASS)
x <- as.matrix(fgl[1:20, 2:9])
x <- x / rowSums(x)
alfadist(x, 0.1)
alfadist(x, 1)
# }