The alpha-distance | R Documentation |

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

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

`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 |

`type` |
Which type distance do you want to calculate after the |

`square` |
In the case of the Euclidean distance, you can choose to return the squared distance by setting this TRUE. |

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

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.

Michail Tsagris.

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

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) x <- as.matrix(fgl[1:20, 2:9]) x <- x / rowSums(x) alfadist(x, 0.1) alfadist(x, 1)

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