The Information Bottleneck Revisited or How to Choose a Good Distortion Measure

It is well-known that the information bottleneck method and rate distortion theory are related. Here it is described how the information bottleneck can be considered as rate distortion theory for a family of probability measures where information divergence is used as distortion measure. It is shown that the information bottleneck method has some properties that are not shared with rate distortion theory based on any other divergence measure. In this sense the information bottleneck method is unique.