The notion of metric plays a key role in machine learning problems such as classification, clustering or ranking. However, it is worth noting that there is a severe lack of theoretical guarantees that can be expected on the generalization capacity of
the classifier associated to a given metric. The theoretical framework of $(epsilon, gamma, tau)$-good similarity functions (Balcan et al., 2008) has been one of the first attempts to draw a link between the properties of a similarity function and those of a linear classifier making use of it. In this paper, we extend and complete this theory by providing a new generalization bound for the associated classifier based on the algorithmic robustness framework.
