TY  - JOUR
AU  - Fazeny, Ariane
AU  - Tenbrinck, Daniel
AU  - Lukin, Kseniaa
AU  - Burger, Martin
TI  - Hypergraph p-Laplacians and Scale Spaces
JO  - Journal of mathematical imaging and vision
VL  - 66
IS  - 4
SN  - 0924-9907
CY  - Dordrecht [u.a.]
PB  - Springer Science + Business Media B.V
M1  - PUBDB-2023-06383
SP  - 529-549
PY  - 2024
N1  - The funding should include  SFB TR 154, Subproject C06, but it was not possible to find it in the mask.
AB  - The aim of this paper is to revisit the definition of differential operators on hypergraphs, which are a natural extension of graphs in systems based on interactions beyond pairs. In particular, we focus on the definition of Laplacian and p-Laplace operators for oriented and unoriented hypergraphs their basic properties, variational structure, and their scale spaces.        We illustrate that diffusion equations on hypergraphs are possible models for different applications such as information flow on social networks or image processing. Moreover, the spectral analysis and scale spaces induced by these operators provide a potential method to further analyze complex data and their multiscale structure.     The quest for spectral analysis and suitable scale spaces on hypergraphs motivates in particular a definition of differential operators with trivial first eigenfunction and thus more interpretable second eigenfunctions. This property is not automatically satisfied in existing definitions of hypergraph p-Laplacians and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001207094300001
DO  - DOI:10.1007/s10851-024-01183-0
UR  - https://bib-pubdb1.desy.de/record/597028
ER  -