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

arXiv:2405.01109v1 Announce Type: cross
Abstract: As a generalization of graphs, hypergraphs are widely used to model higher-order relations in data. This paper explores the benefit of the hypergraph structure for the interpolation of point cloud data that contain no explicit structural information. 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. We prove the variational consistency between the hypergraph $p$-Laplacian regularization and the continuum $p$-Laplacian regularization in …

abstract arxiv benefit cloud cloud data cs.lg cs.na data graphs hypergraph information interpolation math.ap math.na paper regularization relations type