Coal elemental (compositional) data analysis with hierarchical clustering algorithms

The modes of occurrence for elements in coal are extremely important for deciphering geological process of coal formation and for anticipating the technological behavior and environmental and health impacts derived from coal utilization. Hierarchical clustering algorithm has been widely adopted to investigate the modes of occurrence of elements in coal. The traditional statistics (e.g., Pearson correlation, Euclidean distance) for the elemental data of coal may lead to misinterpretation because the elemental data of coal are of compositional nature and follow the rules of Aitchison geometry. This work applied log-ratio transformations in order to overcome this problem. Different hierarchical clustering algorithms with various data transformations can infer modes of occurrence for coal elements, but which algorithm is optimum deserves to be investigated. In this paper, we discuss four commonly used hierarchical clustering algorithms utilizing pivot coordinates and weighted symmetric pivot coordinates (WSPC), two types of log-ratio transformations, to infer modes of occurrence of elements in coal, based on published coal elemental data. Results showed that the Pearson correlation produces more meaningful results than the Euclidean distance in clustering rare earth elements and Y. WSPC produces more interpretable results than those from pivot coordinates transformed data for these coal elemental data. Compared with the single, complete, and centroid, the average-linkage algorithm is indeed the optimum.

Automated summary

The modes of occurrence of elements in coal are crucial for understanding coal formation and predicting impacts from coal utilization. Log-ratio transformations in hierarchical clustering algorithms are effective in inferring these modes of occurrence.