Fuzzy Clustering with Spatial Correction and Its Application to Geometallurgical Domaining

This paper describes a proposed method for clustering attributes on the basis of their spatial variability and the uncertainty of cluster membership. The method is applied to geometallurgical domaining in mining applications. The main objective of geometallurgical clustering is to ensure consistent feed to a processing plant by minimising transitions between different types of feed coming from different domains (clusters). For this purpose, clusters should contain not only similar geometallurgical characteristics but also be located in as few contiguous and compact spatial locations as possible so as to maximise the homogeneity of ore delivered to the plant. Most existing clustering methods applied to geometallurgy have two problems. Firstly, they are unable to differentiate subsets of attributes at the cluster level and therefore cluster membership can only be assigned on the basis of exactly identical attributes, which may not be the case in practice. Secondly, as they do not take account of the spatial relationships they can produce clusters which may be spatially dispersed and/or overlapped. In the work described in this paper a new clustering method is introduced that integrates three distinct steps to ensure quality clustering. In the first step, fuzzy membership information is used to minimise compactness and maximise separation. In the second step, the best subsets of attributes are defined and applied for domaining purposes. These two steps are iterated to convergence. In the final step a graph-based labelling method, which takes spatial constraints into account, is used to produce the final clusters. Three examples are presented to illustrate the application of the proposed method. These examples demonstrate that the proposed method can reveal useful relationships among geometallurgical attributes within a clear and compact spatial structure. The resulting clusters can be used directly in mine planning to optimise the ore feed to be delivered to the processing plant.