Unsupervised classification of multivariate geostatistical data: Two algorithms

Abstract

International audienceWith the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset

A spectral clustering approach for multivariate geostatistical data

“…The second baseline method (M2) is the traditional spectral clustering based on the fully connected graph [36]. The third baseline method (M3) is the spectral clustering based on k-nearest spatial neighbour graph [39]. The fourth baseline method is the spectral clustering (M4) based on the Delaunay graph [39].…”

“…The third baseline method (M3) is the spectral clustering based on k-nearest spatial neighbour graph [39]. The fourth baseline method is the spectral clustering (M4) based on the Delaunay graph [39]. In all these benchmark clustering methods, geographical coordinates are considered as attributes.…”

“…The second group uses existing non-spatial clustering methods by modifying the dissimilarity and/or similarity measure between two observations to take explicitly into account the spatial dependence [6,17,19,37]. The third group enforces the spatial contiguity during the clustering process [38,39]. The latest group relies on the assumption that observations are drawn from a particular distribution like a mixture of Gaussian or Markov random fields [1][2][3][4]14,21].…”

Improving Automated Geological Logging of Drill Holes by Incorporating Multiscale Spatial Methods

“…In previous studies, ML methods have been modified to include 3D spatial information for sets of dense drill hole data, such as brownfields exploration or mining situations. For example, the method of Fouedjio et al (2017) uses geostatistical parameters to encode the joint spatial continuity structure of multiple variables, Romary et al (2015) include spatial proximity as a condition for clustering and Bubnova et al (2020) uses spatial data as a connectivity constraint for clustering. All these methods have been developed and tested for dense drilling situations and are less reliable in greenfields mineral exploration because of the large distances between drill holes.…”

Fuzzy Clustering with Spatial Correction and Its Application to Geometallurgical Domaining

“…This method takes into account the membership of all neighbours of any observation for clustering. Romary et al (2015) incorporated the spatial component into the distance metric using a hierarchical clustering method. The distance function takes into account the spatial connectivity introduced by a moving neighbourhood.…”