Defining geologic domains using cluster analysis and indicator correlograms: a phosphate-titanium case study

Abstract

One of the first decisions to be made when building a mineral resource model is the definition of geological/geostatistical domains. Cluster analysis is a set of techniques in machine learning that can be especially suited for this matter. In order to compare different approaches, two clustering algorithms were investigated in this study: k-means and the dual-space clustering algorithm. Choosing the most appropriate method and the number of clusters can be challenging and some metrics are needed to support these decisions, including the validation of the spatial distribution of the clusters, which is not always appropriately discussed in the literature. We introduce the use of correlograms of the indicators for that matter. Although clustering techniques can be robust for an application in resource modelling, expert knowledge is still necessary when applying cluster analysis to resource modeling, since final decisions should not be based solely on statistical indexes, but also on experience. In this paper, the proposed methodology was tested in a threedimensional dataset related to a phosphate/titanium deposit.

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

“…The conventional procedure for defining mineral resource estimation domains follows a methodology based on the integration of geological studies and statistical analysis [11,12]. This approach is firmly rooted in geological understanding and hu-man intervention, carried out through a series of stages, from selecting the geological attributes controlling the mineral grade to geological, statistical, and geostatistical validation of the estimation domains [13,14].…”

Geometallurgical Responses on Lithological Domains Modelled by a Hybrid Domaining Framework

“…In another example, Séguret [22] developed a "partial grade" estimation method to identify the border effect between domains. There are also hybrid approaches that use geostatistical and machine learning algorithms (e.g., classification and clustering) to predict the boundaries of geological and geometallurgical domains [23][24][25][26][27]. However, most of these domaining methods use one deterministic inter-operation, and thus the uncertainty of the domain boundaries may not be fully quantified [23,28].…”

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

“…Clustering algorithms have been used since the 1960s, when Sokal et al [7] introduced the hierarchical agglomerative technique to work in the field of taxonomy, and MacQueen [8] introduced the k-means algorithm. This approach may be especially appropriate for the definition of estimation domains, since it divides the data into groups based on the relationships between the more relevant variables of the problem [9]. Automatic grouping is an approach to analyze spatial data at a higher level of abstraction by grouping according to their similarity into significant groups [10].…”

“…In [17], the k-means method is used to define geo-metallurgical domains in an iron deposit in northeastern Iran, using data from laboratory analysis (Fe, FeO, S), magnetic susceptibility, and spatial coordinates (X, Y, Z). Moreira et al [9] used k-means to define estimation geological domains in a phosphate-titanium deposit, mainly using data from laboratory analysis (P 2 O 5 , TiO 2 , and CaO), rock type, and alteration. However, k-means optimizes a cost function defined on the Euclidean distance measure between data points and means.…”