This book is by no means exhaustive. There are many issues related to the analysis of compositional data, which have not been included in an attempt to limit its length. Other issues, closely related to the methods presented before, are still a matter of active research. They are briefly discussed here, and some references are included to guide the interested reader to relevant literature.
One major issue in the analysis of compositions is the selection of an orthonormal basis. The most straightforward way to do this is to calculate principal components of -transformed compositions. But the resulting components usually involve all parts, making it difficult to interpret them. In an attempt to approximate principal components taking advantage of the interpretability of balances obtained through a sequential binary partition (SBP), principal balances were defined by Pawlowsky-Glahn et al. (2011). Three initial, suboptimal algorithms have been proposed. Approaches based on sparse principal components were studied in (Mert et al., 2014). Some of these algorithms are available in the
R-package “compositions” (Boogaart and Tolosana-Delgado, 2013).
Robustness is a general issue of statistics, related to the presence of contaminated or atypical samples, that is, of outliers. Roughly speaking, an outlier is ...