A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature.

翻译：度量关系根据定义是对称的。由于许多数据集是非对称的，本文发展了一套关于非对称成本函数的系统理论。中间性关系在其中扮演重要角色。我们还在非对称设定下引入了Dress群的概念，并指出了一种曲率概念。