  Diffuse interface methods have recently been introduced for the task of
semi-supervised learning. The underlying model is well-known in materials
science but was extended to graphs using a Ginzburg--Landau functional and the
graph Laplacian. We here generalize the previously proposed model by a
non-smooth potential function. Additionally, we show that the diffuse interface
method can be used for the segmentation of data coming from hypergraphs. For
this we show that the graph Laplacian in almost all cases is derived from
hypergraph information. Additionally, we show that the formerly introduced
hypergraph Laplacian coming from a relaxed optimization problem is well suited
to be used within the diffuse interface method. We present computational
experiments for graph and hypergraph Laplacians.
