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When dealing with environmental problems, it is of fundamental importance to establish reference values (geochemical baselines) against which to determine the presence or absence of active contamination processes. In the effort to develop a method to assess the geochemical baselines for territories featuring complex geological settings and a well-established anthropic environmental pressure, we combined compositional data analysis (CoDA) with geolithological information to reduce the degree of uncertainty possibly affecting the results. The proposed approach comprises (1) a knowledge-driven step to select a number of sample subsets from a geochemical dataset each with a high probability of having its composition strongly influenced by only one of the lithologies outcropping in the study area; (2) a data-driven step to compute compositional principal balances and define geochemical indicators to be used to assign each of the observations in the dataset to one of the geochemical domains associated to a mayor lithologies outcropping in the study area; (3) the determination for each geochemical domain of baseline values based on the samples assigned to them by the data-driven step. The method was tested using the geochemical data referring to 887 stream sediment samples collected across the Volturno River catchment basin (Southern Italy), featuring a relevant lithological heterogeneity. The results obtained were easily interpretable as they fitted well with the geomorphological, geochemical, and geodynamic processes characterizing the study area. Despite the use of stream sediments for the specific case study presented, the application principles of the method hold for any environmental media and for any territory for which there is a need to define baseline values. However, for a successful application of the method, it is crucial to have a fair knowledge of the geological settings of the study area. • A novel method to define areas with different natural background is proposed. • A method to build compositional indicators of natural phenomena is proposed. • Indicators are obtained by combining expert knowledge and statistical approaches. • Compositional indicators enable four geochemical domains to be recognized. • Geochemical domains clearly differ from geological units. [ABSTRACT FROM AUTHOR]

Regional mineral exploration is based on geochemical data of which the nature is compositional and frequently involves a large number of components. Consequently, it mostly needs multivariate dimension reduction methods such as principal component analysis (PCA) and its various robust versions. The application of such methods, defined for real random variables, require the data to be represented in coordinates supported in the real space. However, a common problem in exploration geochemistry is to select the appropriate representation. Using centered (clr) and isometric (ilr) logratio coordinates to discriminate anomalous zones for orogeny gold exploration throughout Sweden revealed that there is, as expected, no difference between the two representation methods. The main difference affects the interpretation of the coordinates used. This is observed for regional scale exploration, while it is also needed to study different ways of representing geochemical data in local scale. [Display omitted] • Geochemical data possess a compositional nature, necessitating meaningful representation • Among compositional tools, clr and olr coordinates are used for representation • Extensive till geochemical data from across Sweden were employed for comparison • Both models exhibited strikingly similar results in terms of anomaly separation • The ilr-based model enhanced accuracy in delineating anomalous zones [ABSTRACT FROM AUTHOR]

Instead of looking at individual nutrients or foods, dietary pattern analysis has emerged as a promising approach to examine the relationship between diet and health outcomes. Despite dietary patterns being compositional (i.e. usually a higher intake of some foods implies that less of other foods are being consumed), compositional data analysis has not yet been applied in this setting. We describe three compositional data analysis approaches (compositional principal component analysis, balances and principal balances) that enable the extraction of dietary patterns by using control subjects from the Spanish multicase-control (MCC-Spain) study. In particular, principal balances overcome the limitations of purely data-driven or investigator-driven methods and present dietary patterns as trade-offs between eating more of some foods and less of others. [ABSTRACT FROM AUTHOR]

The log-ratio approach to compositional data (CoDa) analysis has now entered a mature phase. The principles and statistical tools introduced by J. Aitchison in the eighties have proven successful in solving a number of applied problems. The algebraic–geometric structure of the sample space, tailored to those principles, was developed at the beginning of the millennium. Two main ideas completed the J. Aitchison's seminal work: the conception of compositions as equivalence classes of proportional vectors, and their representation in the simplex endowed with an interpretable Euclidean structure. These achievements allowed the representation of compositions in meaningful coordinates (preferably Cartesian), as well as orthogonal projections compatible with the Aitchison distance introduced two decades before. These ideas and concepts are reviewed up to the normal distribution on the simplex and the associated central limit theorem. Exploratory tools, specifically designed for CoDa, are also reviewed. To illustrate the adequacy and interpretability of the sample space structure, a new inequality index, based on the Aitchison norm, is proposed. Most concepts are illustrated with an example of mean household gross income per capita in Spain. [ABSTRACT FROM AUTHOR]