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@ARTICLE{Fazeny:597028,
      author       = {Fazeny, Ariane and Tenbrinck, Daniel and Lukin, Kseniaa and
                      Burger, Martin},
      title        = {{H}ypergraph p-{L}aplacians and {S}cale {S}paces},
      journal      = {Journal of mathematical imaging and vision},
      volume       = {66},
      number       = {4},
      issn         = {0924-9907},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {PUBDB-2023-06383},
      pages        = {529-549},
      year         = {2024},
      note         = {The funding should include SFB TR 154, Subproject C06, but
                      it was not possible to find it in the mask.},
      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.},
      cin          = {FS-CI},
      ddc          = {510},
      cid          = {I:(DE-H253)FS-CI-20230420},
      pnm          = {623 - Data Management and Analysis (POF4-623) / NoMADS -
                      Nonlocal Methods for Arbitrary Data Sources (777826)},
      pid          = {G:(DE-HGF)POF4-623 / G:(EU-Grant)777826},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001207094300001},
      doi          = {10.1007/s10851-024-01183-0},
      url          = {https://bib-pubdb1.desy.de/record/597028},
}