Visualizing high dimensional structures in geochemical datasets using a combined compositional data analysis and Databionic swarm approach

Abstract

Classical tools for exploratory analysis of large geochemical datasets (e.g., cluster analysis, principal component analysis, etc.) have been successfully utilized for decades to understand complex structures and identify natural, multi-dimensional data clusters. More recent development of machine learning algorithms, both supervised and unsupervised, have increasingly been shown to derive deeper insights from complex datasets than older methods. Moreover, geochemists have long recognized that concentration data are compositional and require special mathematical treatment, such as application of Compositional Data Analysis (CoDA) techniques. Proper approaches for linking CoDA and machine learning is an area of active research. Here, we investigate the behavior of trace elements in coal and coal combustion products from a power plant burning Appalachian Basin coals using a combination of CoDa methods and a relatively new tool for visualizing complex multivariate structures, Databionic swarm (DBS). Databionic swarm is an unsupervised method which combines concepts from emergence, self-organization, game theory, and swarm intelligence, and allows for mapping of higher-order structures onto a lower-dimensional output space (2-dimensions in this case). A suggested approach for converting the raw geochemical data to isometric log-ratios is developed for the system and results from DBS and robust PCA are compared and contrasted.Both PCA and DBS results show similar clustering of feed coal (FC) and pulverized coal (PC) samples and bottom ash (BA) with economizer fly ash (EFA) samples. However, within group variation of the samples was relatively difficult to identify in the PCA analysis. Results from DBS show that the BA and EFA samples are geochemically distinguishable based on the relative abundances of As, Cd, and Pb vs. Cr and Ni and As and Cd vs. Pb. Similarly, the PC and FC samples exhibit statistically different Cr vs. Ni ratios, which was not obvious from the PCA scores. Abnormally low Hg to Cl ratios in the fly ash (FA) samples relative to the rest of the samples, provided insight into the preferential removal of Hg vs. Cl, possibly in response to the generation of more gaseous oxidized mercury in the flue gas, owing to elevated Cl concentrations in the coal. Such findings demonstrate that DBS and other machine learning techniques allow for quick visualization of complex geochemical data structures in a way that is both consistent with the principals of CoDA and an improvement over classical methods.