Dirac signal processing of higher-order topological signals
dc.contributor.author | Calmon, L | |
dc.contributor.author | Schaub, MT | |
dc.contributor.author | Bianconi, G | |
dc.date.accessioned | 2023-12-19T14:21:40Z | |
dc.date.available | 2023-12-19T14:21:40Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 1367-2630 | |
dc.identifier.other | ARTN 093013 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/93092 | |
dc.description.abstract | Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also to the links, to the triangles and in general to the higher dimensional simplices of simplicial complexes. These topological signals can describe a large variety of real systems including currents in the ocean, synaptic currents between neurons and biological transportation networks. In real scenarios topological signal data might be noisy and an important task is to process these signals by improving their signal to noise ratio. So far topological signals are typically processed independently of each other. For instance, node signals are processed independently of link signals, and algorithms that can enforce a consistent processing of topological signals across different dimensions are largely lacking. Here we propose Dirac signal processing, an adaptive, unsupervised signal processing algorithm that learns to jointly filter topological signals supported on nodes, links and triangles of simplicial complexes in a consistent way. The proposed Dirac signal processing algorithm is formulated in terms of the discrete Dirac operator which can be interpreted as 'square root' of a higher-order Hodge Laplacian. We discuss in detail the properties of the Dirac operator including its spectrum and the chirality of its eigenvectors and we adopt this operator to formulate Dirac signal processing that can filter noisy signals defined on nodes, links and triangles of simplicial complexes. We test our algorithms on noisy synthetic data and noisy data of drifters in the ocean and find that the algorithm can learn to efficiently reconstruct the true signals outperforming algorithms based exclusively on the Hodge Laplacian. | en_US |
dc.relation.ispartof | NEW JOURNAL OF PHYSICS | |
dc.rights | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. | |
dc.rights | Attribution 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
dc.subject | higher-order networks | en_US |
dc.subject | discrete Dirac operator | en_US |
dc.subject | topological signals | en_US |
dc.subject | signal processing | en_US |
dc.title | Dirac signal processing of higher-order topological signals | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2023 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft | |
dc.identifier.doi | 10.1088/1367-2630/acf33c | |
pubs.author-url | https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:001059516700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=612ae0d773dcbdba3046f6df545e9f6a | en_US |
pubs.issue | 9 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Published | en_US |
pubs.volume | 25 | en_US |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |
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Except where otherwise noted, this item's license is described as Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.