Multidimensional Techniques for Compositional Data Analysis

Abstract

This chapter based on our recent research should represent a novel approach, because, so far, no book has been written on this subject in Earth Sciences, except the widely known classic work of Aitchison (The statistical analysis of compositional data. Chapman and Hall, London, UK, 1986) and a little-known recent book in Spanish by Verma (Análisis estadístico de datos composicionales. Universidad Nacional Autónoma de México, CDMX, 2016). The serious problems with the use of compositional data and ternary diagrams are pointed out. The main objective is to replace ternary diagrams from statistically coherent alternatives based on log-ratio transformations, which has been clearly achieved. The advantage of the fulfillment of the assumption of multi-normality is documented. The methodology presented can be applied to other science or engineering fields. The chapter concludes with a visual explanation of bivariate discordant outliers, which has direct implication with the multivariate discordancy.