arXiv subjects

Eric Grunsky

Publications and source records attributed to Eric Grunsky.

3 recordsLinked to original sources

arXiv2025

Principal Subsimplex Analysis

Compositional data, which are data that lie in a simplex, naturally arise in many scientific domains such as geochemistry, microbiology, and economics. In such domains, obtaining sensible lower-dimensional representations and modes of variation plays an important role. A typical approach to the problem is applying a log-ratio transformation followed by principal component analysis (PCA). However, this approach has several potential weaknesses: it can amplify variation in minor variables and obscure important variation within major variables; it is not directly applicable to datasets containing zeros, and zero imputation methods can give highly variable results; it has limited ability to capture linear patterns present on the simplex. In this paper, we propose novel methods that produce nested sequences of simplices of decreasing dimensions analogous to backwards principal component analysis. These nested sequences offer both interpretable lower dimensional representations and linear modes of variation. In addition, our methods are applicable without any modification to datasets containing zeros. We demonstrate our methods on simulated data and on relative abundances of diatom species during the late Pliocene. Supplementary materials and R implementations for this article are available online.

stat.ME↗

arXiv2023

GeoCoDA: Recognizing and Validating Structural Processes in Geochemical Data. A Workflow on Compositional Data Analysis in Lithogeochemistry

Geochemical data are compositional in nature and are subject to the problems typically associated with data that are restricted to the real non-negative number space with constant-sum constraint, that is, the simplex. Geochemistry can be considered a proxy for mineralogy, comprised of atomically ordered structures that define the placement and abundance of elements in the mineral lattice structure. Based on the innovative contributions of John Aitchison, who introduced the logratio transformation into compositional data analysis, this contribution provides a systematic workflow for assessing geochemical data in a simple and efficient way, such that significant geochemical (mineralogical) processes can be recognized and validated. This workflow, called GeoCoDA and presented here in the form of a tutorial, enables the recognition of processes from which models can be constructed based on the associations of elements that reflect mineralogy. Both the original compositional values and their transformation to logratios are considered. These models can reflect rock-forming processes, metamorphism, alteration and ore mineralization. Moreover, machine learning methods, both unsupervised and supervised, applied to an optimized set of subcompositions of the data, provide a systematic, accurate, efficient and defensible approach to geochemical data analysis. The workflow is illustrated on lithogeochemical data from exploration of the Star kimberlite, consisting of a series of eruptions with five recognized phases.

physics.geo-ph↗

arXiv2022

Aitchison's Compositional Data Analysis 40 Years On: A Reappraisal

The development of John Aitchison's approach to compositional data analysis is followed since his paper read to the Royal Statistical Society in 1982. Aitchison's logratio approach, which was proposed to solve the problematic aspects of working with data with a fixed sum constraint, is summarized and reappraised. It is maintained that the properties on which this approach was originally built, the main one being subcompositional coherence, are not required to be satisfied exactly -- quasi-coherence is sufficient, that is near enough to being coherent for all practical purposes. This opens up the field to using simpler data transformations, such as power transformations, that permit zero values in the data. The additional property of exact isometry, which was subsequently introduced and not in Aitchison's original conception, imposed the use of isometric logratio transformations, but these are complicated and problematic to interpret, involving ratios of geometric means. If this property is regarded as important in certain analytical contexts, for example unsupervised learning, it can be relaxed by showing that regular pairwise logratios, as well as the alternative quasi-coherent transformations, can also be quasi-isometric, meaning they are close enough to exact isometry for all practical purposes. It is concluded that the isometric and related logratio transformations such as pivot logratios are not a prerequisite for good practice, although many authors insist on their obligatory use. This conclusion is fully supported here by case studies in geochemistry and in genomics, where the good performance is demonstrated of pairwise logratios, as originally proposed by Aitchison, or Box-Cox power transforms of the original compositions where no zero replacements are necessary.

stat.ME↗