The problem of multivariate classification of samples with radial (or V-shaped) chemical data

On the basis of the results of previous studies, the problem of multivariate classification in the presence of the so-called radial or V-shaped data has been briefly re-examined. Taking into account that the radial data, in the absence of preliminary transformations, usually lead to classifications of samples meaningless from a chemical point of view, five different data transformations have been evaluated and compared in the case of both hypothetical and real samples (real samples, in particular, consisted of archaeological ceramic shards to be classified on the basis of provenance). The following transformations have been used: closure to 100, log row centering, log double centering, row centering, and double centering. The transformed data were then classified by means of hierarchical clustering and principal component analysis (PCA). It has been demonstrated that only the first three transformations lead to correct classifications of radial data, and the causes of this fact have been explained.