Traditional methods for motion comparison consider features from individual characters. However, the semantic meaning of many human activities is usually defined by the interaction between them, such as a high-five interaction of two characters. There is little success in adapting interaction-based features in activity comparison, as they either do not have a fixed topology or are in high dimensional. In this paper, we propose a unified framework for activity comparison from the interaction point of view. Our new metric evaluates the similarity of interaction by adapting the Earth Mover's Distance onto a customized geometric mesh structure that represents spatial-temporal interactions. This allows us to compare different classes of interactions and discover their intrinsic semantic similarity. We created five interaction databases of different natures, covering both two-characters (synthetic and real-people) and character-object interactions, which are open for public uses. We demonstrate how the proposed metric aligns well with the semantic meaning of the interaction. We also apply the metric in interaction retrieval and show how it outperforms existing ones. The proposed method can be used for unsupervised activity detection in monitoring systems and activity retrieval in smart animation systems.