DUGi

Measuring Subcompositional Incoherence

http://dugi.udg.edu/item/http:@@@@hdl.handle.net@@2072@@273628

Subcompositional coherence is a fundamental property of Aitchison’s approach to compositionaldata analysis, and is the principal justification for using ratios of components. For dimensionreduction of a matrix of compositional data, either an unweighted (Aitchison & Greenacre 2002) orweighted (Greenacre & Lewi 2009; Greenacre 2010a: chapter 7) form of log-ratio analysis can beused, and these are both subcompositionally coherent. Many alternative methods that might beapplied to compositional data are subcompositionally incoherent, but some can be judged to be lessincoherent than others. In other words, either for a particular data set, or in general, a method mightactually be quite subcompositionally “robust” in that its results for a subcomposition are quite closeto its results for the same components as part of a full composition. So we propose that lack of subcompositional coherence, that is subcompositional incoherence,can be measured in an attempt to evaluate whether any given technique is close enough, for allpractical purposes, to being subcompositionally coherent. This opens up the field to alternativemethods, which might be better suited to cope with problems such as data zeros and outliers, whilebeing only slightly incoherent

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada