Machine learning-based prediction of trace element concentrations using data from the Karoo large igneous province and its application in prospectivity mapping

Data-Driven Predictive Modeling of Lithofacies and Fe In-Situ Grade in the Assen Fe Ore Deposit of the Transvaal Supergroup (South Africa) and Implications on the Genesis of Banded Iron Formations

“…The centered logratio (clr) transformation is a popular choice in traditional multivariate compositional data analysis (Aitchison, 1982;Grunsky et al, 2014;Harris et al, 2015;Chen et al, 2018;Grunsky & de Caritat, 2019), which takes a logarithm of the ratio of all sample compositions by their geometric mean. In previous studies (e.g., Zhang et al, 2021Zhang et al, , 2022, clr-transformed and raw data were empirically demonstrated to produce a similar performance for classification and regression tasks (over a range of algorithms) that are similar to those used in this study. However, since our data were frequently missing FeO and MgO (and other elements to lesser extents, such as S), it is unclear whether the clr transformation would be effective if Fe were substituted for FeO.…”

“…In this study, we employed the following algorithms: k-nearest neighbors (Tikhonov, 1943;kNN, Fix & Hodges, 1951;Cover & Hart, 1967; Elastic-Net (for regression), Santosa & William, 1986;Tibshirani, 1996;Witten & Frank, 2005;Zou & Hastie, 2005 Gaussian Process, Rasmussen & Williams, 2006;Kotsiantis, 2007); support vector machines (Vapnik, 1998;Hsu & Lin, 2002;Karatzoglou et al, 2006); tree-based algorithms such as random forest and adaptive boosting or AdaBoost (Ho, 1995;Breiman, 1996aBreiman, , 1996bFreund & Schapire, 1997;Breiman, 2001a;Kotsiantis, 2014;Sagi & Rokach, 2018); logistic regression (for classification), Cramer, 2002); naı ¨ve Bayes (for classification, Rennie et al, 2003;Hastie et al, 2009); and artificial neural network (ANN, Curry, 1944;Rosenblatt, 1961;Rumelhart et al, 1986;Hastie et al, 2009;Lemare ´-chal, 2012). For details of these algorithms aside from Gaussian Process, their functionality and parameters, as well as for two application examples that are similar to those of this study, see Zhang et al (2021Zhang et al ( , 2022. For Gaussian Process, details can be found in Rasmussen and Williams (2006).…”

“…Predictive modeling with geochemical data can be done using both supervised and unsupervised machine learning methods. Data are unlabeled in unsupervised learning, which means class labels (such as concentrations or rock types) are unavailable, and the machine attempts to deduce categorizations within the data to develop a classification scheme, which is then used to categorize fresh data (Hastie et al, 2009;Zhang et al, 2021Zhang et al, , 2022. The data were labeled (for example, an elemental concentration is recorded) and utilized to tune the algorithm's hyperparameters using training and cross-validation datasets in supervised learning (Hastie et al, 2009).…”

“…The data were labeled (for example, an elemental concentration is recorded) and utilized to tune the algorithm's hyperparameters using training and cross-validation datasets in supervised learning (Hastie et al, 2009). The tuned models are used to regress continuous (e.g., an element's concentration) or discrete (e.g., rock kinds) labels (Zhang et al, 2021(Zhang et al, , 2022. Data that do not overlap with the training and cross-validation datasets can be used to evaluate model performance.…”

“…The irreducible component of the prediction error is noise. Given that algorithms often exhibit diverse bias-variance behaviors, the selection of a suitable algorithm for a particular job is sometimes meant to intentionally raise bias for a correspondingly bigger reduction in variance, which promotes model generalizability (Zhang et al, 2021(Zhang et al, , 2022.…”