Journal Article

PUBDB-2023-06383

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Hypergraph p-Laplacians and Scale Spaces

Fazeny, A. (Corresponding author)DESY* ; Tenbrinck, D. ; Lukin, K. ; Burger, M.DESY*

2024
Springer Science + Business Media B.V Dordrecht [u.a.]

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Please use a persistent id in citations: doi:10.1007/s10851-024-01183-0  doi:10.3204/PUBDB-2023-06383

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.

Note: The funding should include SFB TR 154, Subproject C06, but it was not possible to find it in the mask.

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)
2. NoMADS - Nonlocal Methods for Arbitrary Data Sources (777826) (777826)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; DEAL Springer ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Fazeny, A. (Corresponding author)DESY* ; Tenbrinck, D. ; Lukin, K. ; Burger, M.DESY*
Hypergraph p-Laplacians and Scale Spaces
[10.3204/PUBDB-2023-06362]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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