Finding the number of natural clusters in groundwater data sets using the concept of equivalence class

Abstract Cluster analysis has numerous scientific and practical applications. This paper presents a computer program to find an adequate (natural) number of clusters and to isolate anomalous samples in a data set. The program incorporates an algorithm that is based on the mathematical concept of equivalence class and uses the framework of the graph theory to identify equivalence classes in multivariate data bases. This type of clustering algorithm is particularly useful when one is dealing with groundwater data sets, because anomalies are frequent in these sets, and because the number of groups that are present often are impossible to estimate; the number will depend on the combined effect of many factors, including geology, morphology, climate and pollution. As an example of the utility of this program, a set of groundwater samples is clustered, and the average chemistry of nine identified equivalence classes is related to weathering reactions of plagioclase in a Portuguese granitoid area.

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