Multivariate Modelling of Geometallurgical Variables by Projection Pursuit

The integration of geological and geometallurgical data can significantly improve decision-making and optimize mining production due to a better understanding of the resources and their metallurgical performances. The primary-response rock property framework is an approach to the modelling of geometallurgy in which quantitative and qualitative primary properties are used as proxies of metallurgical responses. Within this framework, primary variables are used to fit regression models to predict metallurgical responses. Whilst primary rock property data are relatively abundant, metallurgical response property data are not, which makes it difficult to establish predictive response relationships. Relationships between primary input variables and geometallurgical responses are, in general, complex, and the response variables are often non-additive which further complicates the prediction process. Consequently, in many cases, the traditional multivariate linear regression models (MLR) of primary-response relationships perform poorly and a better alternative is required for prediction. Projection pursuit is a powerful exploratory statistical modelling technique in which data from a number of variables are projected onto a set of directions that optimize the fit of the model. The purpose of the projection is to reveal underlying relationships. Projection pursuit regression (PPR) fits standard regression models to the projected data vectors. In this paper, PPR is applied to the modelling of geometallurgical response variables. A case study with six geometallurgical variables is used to demonstrate the modelling approach. The results from the proposed PPR models show a significant improvement over those from MLR models. In addition, the models were bootstrapped to generate distributions of feasible scenarios for the response variables. Our results show that PPR is a robust technique for modelling geometallurgical response variables and for assessing the uncertainty associated with these variables.