Process Mineralogy Today

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Working with High-Dimensional Data Part 4: Classifying Unknown Samples using Machine Learning Principles

In the previous articles in this series (part 1, part 2, and part 3) we’ve been performing analyses on an example high-dimensional geochemical data set from a resource feasibility study with the goal of developing a geometallurgical domain model, which could be used for sample selection for more detailed characterisation work and practical mine planning. In this article we continue with this example and take a closer look at how the geometallurgical domains from part 3 guide the grouping of unclassified samples collected from the same resource.

 

In the working example we now have to sample sets: 1) the samples selected for metallurgical screening and chemical assay testing, and 2) the samples selected for head assay testing only. The data from the former set were used in previous articles to develop a metallurgical domain model, and now the latter set needs to be classified according to their geospatial locations. Similar to when we reassigned samples from one domain to another depending on their spatial proximity (see part 3), we compute the spatial relationship between samples that require classification and the samples defining the geometallurgical domains, and then assign the unknown sample to the closest domain. In the field of machine learning the idea of determining the closest reference samples to a test sample is known as computing the “k number of nearest neighbours.” In this example the assumption is that the unknown sample will display similar metallurgical screening behaviour as the geometallurgical domain it is assigned to. Figure 1 is an interactive graph showing the spatial relationships of the unclassified samples and the behaviour domains.

 

Note: click and drag to rotate the graph; select or deselect domains in the legend.

 

 

Now that the unknown samples are classified into existing domains the next task is to determine if the head assays of those samples classified into specific domains have any unique characteristics. A simple way of investigating the head assay data is by plotting the mean chemistry of samples assigned to each domain and visually identifying the key features (figure 2). These unique properties can then be used as “fingerprints” to estimate the geometallurgical behaviour of other samples that are spatially too far from the region where the reference domains are located, but for which head assay data are available. This final step of extrapolating the head assay fingerprints to other unknown samples is also done by computing the “k number of nearest neighbours“, however, in this instance the proximity measure  is based on the geochemistry vectors and not their spatial relationships.

 

Note: click and drag to select an area of the graph; select or deselect domains in the legend.

 

 

I hope you enjoyed this short series of articles. This general workflow is not a groundbreaking development, however, our objective was to work through an example of utilising complex geochemical data (part 1) to construct a geometallurgical domain model (part 2) in its geospatial context (part 3) with the goal of developing a more complete understanding of the most appropriate mining strategy and the potential variance of feed material into the processing plant. The last steps explained in this article show how we can extrapolate the domain information to other unknown samples to better understand the resource at a larger scale and to make predictions about metallurgical behaviour.

 

If you have any feedback or suggestions please feel free to comment below or contact us to start a conversation. This is our last article for the year. Enjoy your festive season, thank you for sticking with us, and we look forward to catching up again in the new year!


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About the Author: Pieter Botha


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