  Hypergraphs allow one to encode higher-order relationships in data and are
thus a very flexible modeling tool. Current learning methods are either based
on approximations of the hypergraphs via graphs or on tensor methods which are
only applicable under special conditions. In this paper, we present a new
learning framework on hypergraphs which fully uses the hypergraph structure.
The key element is a family of regularization functionals based on the total
variation on hypergraphs.
