Inverse of the α-transformation
The inverse of the α-transformation.
alfainv(x, a, h = TRUE)
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 α=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. |
The inverse of the α-transformation is applied to the data. If the data lie outside the α-space, NAs will be returned for some values.
A matrix with the pairwise distances.
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>
Tsagris M.T., Preston S. and Wood A.T.A. (2016). Improved classification for compositional data using the α-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
library(MASS) x <- as.matrix(fgl[1:10, 2:9]) x <- x / rowSums(x) y <- alfa(x, 0.5)$aff alfainv(y, 0.5)
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