Clustering composition vectors using uncertainty information

In the biological and environmental sciences, interest often lies in using multivariate observations to discover natural clusters of objects. In this manuscript, the incorporation of measurement uncertainty information into a cluster analysis is discussed. This study is motivated by a problem involving the clustering of composition vectors associated with each of several chemical species. The observed abundance of each component is available along with its estimated uncertainty (measurement error standard deviation). An approach is proposed for converting the abundance vectors into composition (relative abundance) vectors, obtaining the covariance matrix associated with each composition vector, and defining a Mahalanobis distance between composition vectors that are suitable for cluster analysis. The approach is illustrated using particle size distributions obtained near Houston, Texas in 2000. Computer simulation is used to compare the performance of Mahalanobis‐distance‐based and Euclidean‐distance‐based clustering approaches. The use of a modified Mahalanobis distance along with Ward's method is recommended for use.