Generalizing diffuse interface methods on graphs: non-smooth potentials and hypergraphs
This work provides incremental improvements to semi-supervised learning methods for data segmentation on graphs and hypergraphs.
The authors generalized diffuse interface methods for semi-supervised learning by incorporating non-smooth potentials and extending them to hypergraphs, demonstrating computational experiments with graph and hypergraph Laplacians.
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.