Application of the k-Prototype Clustering Approach for the Definition of Geostatistical Estimation Domains

Abstract

The definition of geostatistical domains is a stage in the estimation of mineral resources, in which a sample resulting from a mining exploration process is divided into zones that show homogeneity or minimal variation in the main element of interest or mineral grade, having geological and spatial meaning. Its importance lies in the fact that the quality of the estimation techniques, and therefore, the correct quantification of the mineral resource, will improve in geostatistically stationary areas. The present study seeks to define geostatistical domains of estimation for a mineral grade, using a non-traditional approach based on the k-prototype clustering algorithm. This algorithm is based on the k-means paradigm of unsupervised machine learning, but it is exempt from the one-time restriction on numeric data. The latter is especially convenient, as it allows the incorporation of categorical variables such as geological attributes in the grouping. The case study corresponds to a hydrothermal gold deposit of high sulfidation, located in the southern zone of Peru, where estimation domains are defined from a historical record of data recovered from 131 diamond drill holes and 37 trenches. The characteristics directly involved were the gold grade (Au), silver grade (Ag), type of hydrothermal alteration, and type of mineralization. The results obtained showed that clustering with k-prototypes is an efficient approach and can be used as an alternative or complement to the traditional methodology.

Application of Autoencoders Neural Network and K-Means Clustering for the Definition of Geostatistical Estimation Domains

“…One of them is its slowness and the need for detailed examination by an expert in the deposit's geology. Furthermore, its subjective nature implies that there may be variations in criteria and interpretations among different experts [15].…”

“…These algorithms allow for more precise and coherent data segmentation, aligning with the fundamental principles of geostatistical estimation. This adaptation enhances the accuracy and reliability of estimates, giving the reference greater relevance and robustness [15]. In addressing the challenges of non-stationarity in geostatistical data, our approach employs Autoencoders alongside K-Means clustering.…”

“…Some examples of numerical variables are mineral grades, location coordinates, and categorical variables include rock type, alteration, and mineralization. Specifically, the K-Means algorithm optimizes a cost function based on the Euclidean distance between data points and their centroids, which limits its direct applicability to numerical data [15][16][17][18][19][20][21][22][23]. This limitation can affect the method's utility for categorical geological variables essential for controlling mineral grade, as they cannot contribute directly to the clustering.…”