Signal processing on higher-order networks: Livin’ on the edge... and beyond

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dc.citation.articleNumber108149
dc.citation.journalTitleSignal Processing
dc.citation.volumeNumber187
dc.contributor.authorSchaub, Michael T.
dc.contributor.authorZhu, Yu
dc.contributor.authorSeby, Jean-Baptiste
dc.contributor.authorRoddenberry, T. Mitchell
dc.contributor.authorSegarra, Santiago
dc.date.accessioned2021-07-08T13:45:56Z
dc.date.available2021-07-08T13:45:56Z
dc.date.issued2021
dc.description.abstractIn this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on simplicial complexes and hypergraphs, two common higher-order network abstractions that can incorporate polyadic relationships. We provide brief introductions to simplicial complexes and hypergraphs, with a special emphasis on the concepts needed for the processing of signals supported on these structures. Specifically, we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and nonlinear processing through neural networks, using these two higher-order network models. In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing. For hypergraphs, we present both matrix and tensor representations, and discuss the trade-offs in adopting one or the other. We also highlight limitations and potential research avenues, both to inform practitioners and to motivate the contribution of new researchers to the area.
dc.identifier.citationSchaub, Michael T., Zhu, Yu, Seby, Jean-Baptiste, et al.. "Signal processing on higher-order networks: Livin’ on the edge... and beyond." <i>Signal Processing,</i> 187, (2021) Elsevier: https://doi.org/10.1016/j.sigpro.2021.108149.
dc.identifier.digital1-s2-0-S0165168421001870-main
dc.identifier.doihttps://doi.org/10.1016/j.sigpro.2021.108149
dc.identifier.urihttps://hdl.handle.net/1911/110995
dc.language.isoeng
dc.publisherElsevier
dc.rightsThis is an open access article under the CC BY license
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleSignal processing on higher-order networks: Livin’ on the edge... and beyond
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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