On the aggregation of compositional data

Compositional data naturally appear in many fields of application. For instance, in chemistry, the relative contributions of different chemical substances to a product are typically described in terms of a compositional data vector. Although the aggregation of compositional data frequently arises in practice, the functions formalizing this process do not fit the standard order-based aggregation framework. This is due to the fact that there is no intuitive order that carries the semantics of the set of compositional data vectors (referred to as the standard simplex). In this paper, we consider the more general betweenness-based aggregation framework that yields a natural definition of an aggregation function for compositional data. The weighted centroid is proved to fit within this definition and discussed to be linked to a very tangible interpretation. Other functions for the aggregation of compositional data are presented and their fit within the proposed definition is discussed.

Automated summary

Compositional data naturally appear in many fields of application. In this paper, a more general betweenness-based aggregation framework is considered for defining an aggregation function for compositional data. The weighted centroid is proven to fit within this definition and has a tangible interpretation. Other functions for the aggregation of compositional data are presented and their fit within the proposed definition is discussed.