Application of semi-supervised fuzzy c-means method in clustering multivariate geochemical data, a case study from the Dalli Cu-Au porphyry deposit in central Iran

Abstract Supervised and unsupervised learning methods are widely used to classify and cluster multivariate geochemical data. Supervised learning methods incorporate training functions to classify the geochemical data, whereas unsupervised learning methods extract hidden structures of the data and assign them to various clusters. A semi-supervised learning method is a hybrid learning method that simultaneously extracts the hidden structure of non-training data and uses training data to improve the clustering analysis. In this research, initially eleven soil geochemical variables associated with the Dalli Cu-Au porphyry deposit, located in the central part of Iran, were selected by using hieratical clustering analysis and expert knowledge. Then, the semi-supervised fuzzy c-means clustering method (ssFCM) was used to separate multivariate soil geochemical anomalies from background for further drilling. The results were compared with the fuzzy c-mean clustering (FCM) analysis applied to the same samples. The fundamental concept of the ssFCM method is similar to the widely used FCM method with the exception that the training data, in this case trenching data, were used as an objective function in the clustering analysis. The soil classification results were validated by using cluster validity indices, cross-validation and the uncertainty measurement. The validation results demonstrated that the ssFCM method was superior in classifying the multivariate soil geochemical data compared to the FCM method. For further validation, the membership values of the favorable classes identified by both FCM and ssFCM methods were converted to grid maps and compared with the spatial distribution of copper anomalies along the trenches and surface projection of the boreholes. This comparison suggests that the favorable multivariate soil geochemical anomalies identified by the ssFCM analysis correlate well with copper mineralization in rock channel and drill core samples.