Fuzzy clustering analysis of compositional data and comparing it with exploratory compositional data dendrogram, case study: Anar region stream sediments geochemistry

Summary: One of the most important methods in unsupervised datamining is clustering that when applied on variables leads to dimension reduction. Among all of them, fuzzy clustering methods are preferred because of special features and better flexibility in partitioning groups. In this study, FANNY algorithm proposed by Kauffmann and Rousseuw has been applied in variable clustering of the geochemical stream sediments that have a compositional nature. Referring to the extensive recent researches and novel methods presented in opening compositional data, another definition of distance is needed for them to be transformed isometrically to the euclidean space to be interpretable with classical operations. In this case study after preparation of geochemical stream sediments data of Anar region in Kerman, first the exploratory dendrogram of the simplex space was plotted and 4 clusters were obtained. Then using fanny algorithm, clr-transformed variables were clustered. It showed an acceptable conformity with the dendrogram results. In case of determining the balances of SBP manually instead of default and with a prior knowledge, the results of exploratory dendrogram would be more precise.
Geochemical exploration based on stream sediment analysis, is one of the most important methods in assessing mineral potentials in prospecting brownfield areas. Different statistical methods have been developed to identify the pattern of groups of associated geochemical elements in the last decades. In this research, stream sediments data clustering of Anar exploratory region have been analyzed with a particular perspective of the closed nature of geochemical datasets using two known methods, fuzzy clustering and exploratory dendrogram.
Methodology and Approaches: First, using R software compositions-package, exploratory dendrogram of compositional data was calculated and plotted based on ward criterion and default sequential binary partition balances in simplex space. Due to applying this method, 4 clusters were detected. Then by applying fanny algorithm (cluster package) –one of the most flexible ones in fuzzy clusterings –on clr- transformed data, 4 clusters with the best silhouette were determined. The fuzzification degree was selected in a way that would be near to crisper methods like dendrogram in order to compare the results.
Results and Although different methods applied on transformed compositional data, their similar results showed very good conformity with lithology and geological structures. It presented a good separation in simplex space. If the balances in SBP are to be defined manually, the reduced dimensions of the variables would be more informative.