Insights in Hierarchical Clustering of Variables for Compositional Data

Abstract

R-mode hierarchical clustering is a method for forming hierarchical groups of mutually exclusive subsets of variables. This R-mode cluster method identifies interrelationships between variables which are useful for variable selection and dimension reduction. Importantly, the method is based on metric elements defined on the sample space of variables. Consequently, hierarchical clustering of compositional parts should respect the particular geometry of the simplex. In this work, the connections between concepts such as distance, cluster representative, compositional biplot, and log-ratio basis are explored within the framework of the most popular R-mode agglomerative hierarchical clustering methods. The approach is illustrated in a paleoecological study to identify groups of species sharing similar behavior.