Applications in Compositional Data Analysis

• Activity Number: 56
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Raimon Tolosana-Delgado*+ and K. Gerald van den Boogaart
• Companies: Helmholtz Institute Freiberg for Resource Technology and Helmholtz Institute Freiberg for Resource Technology
• Keywords: biplot ; PCA ; linear model ; geochemical survey ; clr ; ilr

Abstract

Compositional data occur in all fields of science: from politics to materials engineering, from biomedical sciences to geochemistry. In all these fields, variables representing the relative contribution of some parts forming a whole are routinely acquired. Actually, compositions form their own scale, essentially characterized by their intrinsic multivariate nature and the closure to constant sum to 100%. Statistical techniques used with these data must then conform to that scale.

This contribution presents a comprehensive summary of how to adapt the most common statistical techniques, based on the principle of working on coordinates within the log-ratio approach. In application of this principle, data are represented in an one-to-one set of logratios of the original components, the scores are analysed with classical multivariate tools, and results are eventually back-transformed for interpretation. In particular, this contribution explores the uses of cluster analysis, principal components and linear regression to explain the natural variability on several data sets from the Earth sciences.