Adapted Ward’s Clustering Method: Generalization to Several Variables Using the Fast Fourier Transform

Earth science studies deal in general with multivariate, regionalized, observations, which may be compositional, or not. Frequently, it is of interest to know whether those data have to be divided into different populations, a task usually performed by cluster analysis. This problem cannot be studied with traditional methods because samples are not independent. In that case, an extension of Ward’s clustering method to spatially dependent samples can be used. This methodology is based on a generalized Mahalanobis distance, which uses the covariance and cross covariance (or variogram and cross-variogram) matrices. In its original version, the method was iterative and tedious, as it was necessary to re-estimate the spatial covariance structure at each step. In this work, we stay within the same theoretical framework, but we improve the methodology using the Fast Fourier Transform (FFT) method to find the covariance structure. Thus, we obtain a generalization to many compositional variables of adapted Ward’s clustering method.