# alfainv: Inverse of the alpha-transformation In Compositional: Compositional Data Analysis

 Inverse of the alpha-transformation R Documentation

## Inverse of the α-transformation

### Description

The inverse of the α-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 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@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

### 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). 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

```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)
```

Compositional documentation built on July 8, 2022, 1:06 a.m.