Graph signal processing: Vertex multiplication

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buir.contributor.authorKartal, Bünyamin
buir.contributor.authorKoç, Aykut
buir.contributor.orcidKartal, Bünyamin|0000-0003-3633-2587
buir.contributor.orcidKoç, Aykut|0000-0002-6348-2663
dc.citation.epage1274en_US
dc.citation.spage1270en_US
dc.citation.volumeNumber28en_US
dc.contributor.authorKartal, Bünyamin
dc.contributor.authorBayiz, Y. E.
dc.contributor.authorKoç, Aykut
dc.date.accessioned2022-01-26T13:17:17Z
dc.date.available2022-01-26T13:17:17Z
dc.date.issued2021-06-03
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractOn the Euclidean domains of classical signal processing, linking of signal samples to underlying coordinate structures is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying graph vertices, a major problem in graph signal processing is the lack of explicit association of vertices with an underlying coordinate structure. To make this link, we propose an operation, called the vertex multiplication (VM), which is defined for graphs and can operate on graph signals. VM, which generalizes the coordinate multiplication (CM) operation in time series signals, can be interpreted as an operator that assigns a coordinate structure to a graph. By using the graph domain extension of differentiation and graph Fourier transform (GFT), VM is defined such that it shows Fourier duality that differentiation and CM operations are duals of each other under Fourier transformation (FT). Numerical examples and applications are also presented.en_US
dc.identifier.doi10.1109/LSP.2021.3086391en_US
dc.identifier.eissn1558-2361
dc.identifier.issn1070-9908
dc.identifier.urihttp://hdl.handle.net/11693/76808
dc.language.isoEnglishen_US
dc.publisherIEEEen_US
dc.relation.isversionofhttps://doi.org/10.1109/LSP.2021.3086391en_US
dc.source.titleIEEE Signal Processing Lettersen_US
dc.subjectGraph signal processing (GSP)en_US
dc.subjectGraph fourier transform (GFT)en_US
dc.subjectDualityen_US
dc.subjectCoordinate multiplicationen_US
dc.subjectVertex multiplicationen_US
dc.titleGraph signal processing: Vertex multiplicationen_US
dc.typeArticleen_US
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