Partitional Clustering of Compositional Data with Zeros

Partitional methods for clustering compositional data (CoDa) rely on dissimilarity measures consistent with Aitchison’s principles for log-ratio analysis. While these measures require strictly positive components, many observed compositions contain zero elements that prevent the application of standard CoDa techniques. Elaborating on k-prototypes clustering for mixed attributes, we introduce a novel strategy for clustering compositions in the presence of zeros. The proposed method is specifically designed to handle zeros of any type (including essential ones) concentrated in just one or a few components. We describe the method and illustrate its application on a real data set of energy mix compositions, where essential zeros naturally occur in nuclear power shares for countries that prohibit this source.