In the first part of the talk, I will discuss different viewpoints on local classification of metric data. Next, I will outline how local decisions are aggregated into non-local interacting decisions through regularization. This prepares and motivates the design of a dynamical system on an elementary statistical manifold, called assignment flow, for the contextual classification of metric data given on a graph. In the second part, I will explain recent work on parameter learning from data using a suitable linearization of assignment flows and low-rank exponential integration.