# Generalizing diffuse interface methods on graphs: non-smooth potentials and hypergraphs

arXiv: https://arxiv.org/abs/1611.06094 · HTML: https://mlsanity.com/paper/1611.06094/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2016.

## Built on by (most cited first, 2 of 2)

- [An Empirical Study of Graph-Based Approaches for Semi-Supervised Time Series Classification](https://mlsanity.com/paper/2104.08153/) (2021)
- [Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs](https://mlsanity.com/paper/2501.00389/) (2024)

## Abstract (arXiv)

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.