This is the Euclidean (or Manhattan) distance after the \(\alpha\)-IT-transformation has been applied.
Usage
aitdist(x, a, type = "euclidean", square = FALSE)
aitdista(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 \(\alpha=0\), the isometric log-ratio transformation is applied.
type
Which type distance do you want to calculate after the \(\alpha\)-transformation, "euclidean", or "manhattan".
square
In the case of the Euclidean distance, you can choose to return the squared distance by setting this TRUE.
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.
Details
The \(\alpha\)-IT-transformation is applied to the compositional data first and then the Euclidean
or the Manhattan distance is calculated.
References
Clarotto L., Allard D. and Menafoglio A. (2021). A new class of \(\alpha\)-transformations for the spatial analysis of Compositional Data.
https://arxiv.org/abs/2110.07967