Compositional (version 5.5)

Inverse of the alpha-transformation: Inverse of the \(\alpha\)-transformation

Description

The inverse of the \(\alpha\)-transformation.

Usage

alfainv(x, a, h = TRUE)

Arguments

x

A matrix with Euclidean data. However, they must lie within the feasible, acceptable space. See references for more information.

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 inverse of the isometric log-ratio transformation is applied.

h

If h = TRUE this means that the multiplication with the Helmer sub-matrix will take place. It is set to TRUe by default.

Value

A matrix with the pairwise distances.

Details

The inverse of the \(\alpha\)-transformation is applied to the data. If the data lie outside the \(\alpha\)-space, NAs will be returned for some values.

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). 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, alfadist

Examples

# NOT RUN {
library(MASS)
x <- as.matrix(fgl[1:10, 2:9])
x <- x / rowSums(x)
y <- alfa(x, 0.5)$aff
alfainv(y, 0.5)
# }