Clustering Disjoint HJ-Biplot: A new tool for identifying pollution patterns in geochemical studies

- To develop an algorithm to classify the objects and to search a disjoint partition of variables.
- These proposes are simultaneously achieved by an alternating least-squares algorithm.
- A joint plot of both objects and variables by using HJ-biplot method is also given.
- We applied the methodology to study pollution in surface river sediments.
- We obtained interpretable interactions and excellent groups classifications.

This paper introduces a new mathematical algorithm termed Clustering Disjoint HJ-Biplot (CDBiplot), which searches for the underlying data structure in order to find the best classification of the object groups in a reduced space. To this end, disjoint factorial axes are generated, in which each variable only contributes to the formation of one factorial axis. A graphical representation of the individuals and variables is performed using the HJ-Biplot method. In order to facilitate the use of this new method within any practical context, a function in the language R has been developed. This work applies the CDBiplot to study an environmental geochemistry case involving environmental pollution in river surface sediments. The study focuses on an area close to an important mining and metallurgical site, where sediments share a similar geological origin and chemical composition. The algorithm permitted a detailed study of the geochemical interactions and performed an excellent separation of the samples. Thus, the groups obtained were formed according to a similar geological origin, location, and nature of the anthropogenic inputs based only on chemical composition data. These results allowed clear identification of the sources of pollution and the delimitation of the polluted zones. All things considered, we conclude that the proposed algorithm is a powerful tool for studying environmental geochemistry data sets, and suggest that the application of this methodology be extended to other research fields.