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.

成分数据自然会出现在许多应用领域中。例如，在化学中，通常根据组成数据向量来描述不同化学物质对产品的相对贡献。尽管实际上经常出现成分数据的聚合，但是正式化此过程的功能不适合基于标准订单的聚合框架。这是由于以下事实：没有直观的顺序承载合成数据向量集的语义（称为标准单纯形）。在本文中，我们考虑了更通用的基于中间性的聚合框架，该框架为组成数据提供了聚合函数的自然定义。加权质心被证明符合该定义，并被讨论与非常具体的解释有关。提出了组成成分数据聚合的其他功能，并讨论了它们在建议的定义内的适用性。