Asymmetric empirical similarity

The paper suggests a similarity function for applications of empirical similarity theory in which the notion of similarity is asymmetric. I propose defining similarity in terms of a quasimetric. I suggest a particular quasimetric and explore the properties of the empirical similarity model given this function. The proposed function belongs to the class of quasimetrics induced by skewed norms. Finally, I provide a skewness axiom that, when imposed in lieu of the symmetry axiom in the main result of Billot et al. (2008), characterizes an exponential similarity function based on a skewed norm.