Principal coordinate analysis using the alpha-distance {Compositional} R Documentation

## Principal coordinate analysis using the α-distance

### Description

Principal coordinate analysis using the α-distance.

### Usage

```alfa.mds(x, a, k = 2, eig = TRUE)
```

### Arguments

 `x` A matrix with the compositional data. Zero values are allowed. `a` The value of a. In case of zero values in the data it has to be greater than 1. `k` The maximum dimension of the space which the data are to be represented in. This can be a number between 1 and D-1, where D denotes the number of dimensions. `eig` Should eigenvalues be returned? The default value is TRUE.

### Details

The function computes the α-distance matrix and then plugs it into the classical multidimensional scaling function in the "cmdscale" function.

### Value

A list with the results of "cmdscale" function.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

Cox, T. F. and Cox, M. A. A. (2001). Multidimensional Scaling. Second edition. Chapman and Hall.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.

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

```esov.mds, alfa.pca, ```
```  x <- as.matrix(iris[, 1:4])