Title: Classification of compositional data with selective pivot coordinates
Authors: Karel Hron - Palacky University (Czech Republic) [presenting]
Julie Rendlova - Palacky University (Czech Republic)
Peter Filzmoser - Vienna University of Technology (Austria)
Abstract: In classification tasks with geochemical of chemometric data, it frequently happens that observations are of relative (compositional) nature. The logratio approach to compositional data analysis offers a concise methodology by replacing the original scale-invariant positive data by reasonable real variables. The preferred type of such logratio variables corresponds to orthonormal coordinates where the first coordinate aggregates all logratios with the specific part of interest and can be thus linked to that component - we refer to so-called pivot coordinates. However, including all respective logratios into the first pivot coordinate may lead to an artificial occurrence of false positives in biomarker detection. Therefore, we propose a method excluding aberrant logratios so that the coordinate which is afterwards considered to be the pivot one in the resulting coordinate system contains already just the ``cleaned'' information about the relative dominance of the specific component. Importantly, the alternative choice of pivot coordinates, which we suggest to call selective pivot coordinates, does not influence the quality of classification itself since both coordinate systems are just rotations of each other. The effect of such a choice of coordinates will be presented with the partial least squares regression - discriminant analysis of metabolomic data.