Hypergraph $p$-Laplacian regularization on point clouds for data interpolation

no code implementations • 2 May 2024 • Kehan Shi, Martin Burger

We define the $\varepsilon_n$-ball hypergraph and the $k_n$-nearest neighbor hypergraph on a point cloud and study the $p$-Laplacian regularization on the hypergraphs.

Continuum limit of $p$-biharmonic equations on graphs

no code implementations • 30 Apr 2024 • Kehan Shi, Martin Burger

This paper studies the $p$-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$-Laplacian from the perspective of hypergraph.