Clustering compositional data trajectories: the case of particulate matter in the lower troposphere

Trajectories of compositional data, that is sequences of composition measurements taken along a domain, can be considered as functional data. The present work centres on a way of clustering compositional data trajectories. Functional Cluster Analysis (FCA) has been applied in several fields but has not been extended to cope with the problem of clustering compositional data trajectories. In this work, we extend FCA techniques to the analysis of compositional data using suitable compositional algebra both for smoothing observed trajectories and for building suitable metrics to evaluate dissimilarities between objects. When the focus is on the identification of typical shapes, clustering based on derivatives is the most suitable tool. As a motivating example, we consider clustering particulate matter vertical profiles in the lower troposphere. The impact of the choice of metric on the clustering structure is thoroughly discussed in this case study. Copyright © 2011 John Wiley & Sons, Ltd.