Inverse of the alpha-transformation {Compositional}

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.

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.

Value

A matrix with the pairwise distances.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

Tsagris M. and Stewart C. (2022). A Review of Flexible Transformations for Modeling Compositional Data. In Advances and Innovations in Statistics and Data Science, pp. 225–234. https://link.springer.com/chapter/10.1007/978-3-031-08329-7_10

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, alfadist

Examples

library(MASS)
x <- as.matrix(fgl[1:10, 2:9])
x <- x / rowSums(x)
y <- alfa(x, 0.5)$aff
alfainv(y, 0.5)