Principal coordinate analysis using the alpha-distance | R Documentation |

Principal coordinate analysis using the *α*-distance.

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

`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 |

`eig` |
Should eigenvalues be returned? The default value is TRUE. |

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

A list with the results of "cmdscale" function.

Michail Tsagris.

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

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]) x <- x/ rowSums(x) a <- esov.mds(x)

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