The alpha-distance {Compositional} R Documentation

## The α-distance

### Description

This is the Euclidean (or Manhattan) distance after the α-transformation has been applied.

### Usage

```alfadist(x, a, type = "euclidean", square = FALSE)
alfadista(xnew, x, a, type = "euclidean", square = FALSE)

```

### Arguments

 `xnew` A matrix or a vector with new compositional data. `x` A matrix with the compositional data. `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 isometric log-ratio transformation is applied. `type` Which type distance do you want to calculate after the α-transformation, "euclidean", or "manhattan". `square` In the case of the Euclidean distance, you can choose to return the squared distance by setting this TRUE.

### Details

The α-transformation is applied to the compositional data first and then the Euclidean or the Manhattan distance is calculated.

### Value

For "alfadist" a matrix including the pairwise distances of all observations or the distances between xnew and x. For "alfadista" a matrix including the pairwise distances of all observations or the distances between xnew and x.

### Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris mtsagris@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. 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

```alfa, alfainv, alfa.reg, esov ```
```library(MASS)