Inverse of the α-transformation

Description

The inverse of the α-transformation.

Usage

1
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 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.

Details

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.

Value

A matrix with the pairwise distances.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

References

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). 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, alfadist

Examples

1
2
3
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library(MASS)
x <- fgl[1:10, 2:9]
y <- alfa(x, 0.5)$aff
alfainv(y, 0.5)

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