Questions tagged [aitchison-geometry]

Background Compositional data ($x_i>0, \sum_i x_i=c$) are usually analyzed using some kind of log-transformation (alr/clr/ilr), to take into account naturally the fact that, in presence of the sum constraint, only the scaling of data values are of…

I am dealing with compositional data, in a high dimension. Each sample I have behaves like: $$ {S}^D=\left\{\mathbf{x}=[x_1,x_2,\dots,x_D]\in\mathbb{R}^D \,\left|\, x_i>0,i=1,2,\dots,D; \sum_{i=1}^D x_i=1 \right. \right\} $$ In order to embed the…

If one wanted to construct a simple pairwise correlation matrix from an compositional data table using an ILR transform preprocessing step, would this usage violate any assumptions with the transform? Is it valid to use the ILR transform with…