Compositional data analysis -- linear algebra, visualization and interpretation

TL;DR

This paper discusses methods for analyzing compositional data, focusing on linear algebra, visualization, and interpretation techniques, especially for high-dimensional 'omics' data using logratios.

Contribution

It provides a comprehensive overview of linear algebraic approaches, visualization strategies, and interpretative methods tailored for compositional data analysis.

Findings

Logratio transformations facilitate analysis of compositional data.

Visualization techniques improve interpretation of high-dimensional compositional data.

Matrix-vector representations are essential for computation and interpretation.

Abstract

Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100\%. These are data often found in biochemistry and geochemistry, but also in the social sciences, when relative values are of interest rather than the raw values. Recent applications are in the area of very high-dimensional "omics" data. Logratios are frequently used for this type of data, i.e. the logarithms of ratios of the components of the data vectors. These ratios raise interesting issues in matrix-vector representation, computation and interpretation, which will be dealt with in this chapter.