Hypergraph p-Laplacians and Scale Spaces
Fazeny A, Tenbrinck D, Lukin K, Burger M (2024)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2024
Journal
URI: https://link.springer.com/article/10.1007/s10851-024-01183-0
DOI: 10.1007/s10851-024-01183-0
Open Access Link: https://link.springer.com/article/10.1007/s10851-024-01183-0
Abstract
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.
Authors with CRIS profile
Ariane Fazeny
Sonderforschungsbereich/Transregio 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Daniel Tenbrinck
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Martin Burger
Involved external institutions
Germany (DE)How to cite
APA:
Fazeny, A., Tenbrinck, D., Lukin, K., & Burger, M. (2024). Hypergraph p-Laplacians and Scale Spaces. Journal of Mathematical Imaging and Vision. https://doi.org/10.1007/s10851-024-01183-0
MLA:
Fazeny, Ariane, et al. "Hypergraph p-Laplacians and Scale Spaces." Journal of Mathematical Imaging and Vision (2024).
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