Determining the number of groups in geochemical data set using pattern recognition indices on the basis of separation and compactness of clusters

This paper presents an innovative approach for calculating the correct number of groups in the geochemical data sets. The proposed method reduces the uncertainty of traditional methods that is often based on expert knowledge or application of a unique index. On the basis of separation and compactness of clusters, several pattern recognition indices (thirty indices) are used to produce the response distribution. Then, the optimal solution is concluded from the possible answers which are selected on the basis of the maximum frequency of distribution. This process has been implemented on a simulated data set which ultimately has been managed to properly identify the true number of artificial clusters. It has also been applied to a real geochemical data set, and consequently, three clusters are estimated as the optimum group numbers in the data set. The three groups resulted from data clustering are fully correlated with the geological and geochemical evidences in the study area. Partitioning of the heterogeneous data set into homogeneous subsets is an important goal of geochemical data processing which clustering tools are usually used to achieve this goal. Nevertheless, the most important practical challenge in this regard is an estimation of the actual number of underlying groups in the data set. This is traditionally related to descriptive geochemical information, expert knowledge, and unique statistical index. Due to the instability and uncertainty of the mentioned approaches, we recommend solving the problem by implementing the whole range of indices, creating a distribution of possible responses and consequently extracting the best answer. To evaluate the performance of the proposed approaches, we generated a two-dimensional simulated data set containing four artificial clusters. The real geochemical data set that is used in this research includes 149 soil samples collected from the North Dalli porphyry Cu-Au deposit, located in Markazi province. Thirty indices were used to determine the optimal number of groups in the data set. These indices were essentially achieved from pattern recognition and their performance is based on maximizing the within-group separation and minimizing the between-group compactness. All indices were implemented in the R programming environment. The mode of response distribution in the case of simulated data was in compliance with the true number of artificial clusters. In case of the geochemical data set of the Dalli Cu-Au deposit, three clusters were identified. Clustering of geochemical data into these three groups indicated a clear geochemical zonation, which corresponds to the geological and mineralogical evidences in the study area.