Signals on graphs : transforms and tomograms

Detalhes bibliográficos
Autor(a) principal: Mendes, R. Vilela
Data de Publicação: 2016
Outros Autores: Mendes, Hugo C., Araújo, Tanya
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/29455
Resumo: Development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presen
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spelling Signals on graphs : transforms and tomogramsNetwork SignalsGraph-TransformsTomogramsDynamics on NetworksDevelopment of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presenElsevierRepositório da Universidade de LisboaMendes, R. VilelaMendes, Hugo C.Araújo, Tanya2023-11-21T11:38:14Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29455engMendes, R. Vilela; Hugo C. Mendes and Tanya Araújo. (2016). ”Signals on graphs: transforms and tomograms”. Physica A: Statistical Mechanics and its Applications, Volume 50 .(Search PDF in 2023).0378-4371dx.doi.org/10.1016/j.physa.2016.01.002info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-26T01:31:54Zoai:www.repository.utl.pt:10400.5/29455Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:19:47.799308Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Signals on graphs : transforms and tomograms
title Signals on graphs : transforms and tomograms
spellingShingle Signals on graphs : transforms and tomograms
Mendes, R. Vilela
Network Signals
Graph-Transforms
Tomograms
Dynamics on Networks
title_short Signals on graphs : transforms and tomograms
title_full Signals on graphs : transforms and tomograms
title_fullStr Signals on graphs : transforms and tomograms
title_full_unstemmed Signals on graphs : transforms and tomograms
title_sort Signals on graphs : transforms and tomograms
author Mendes, R. Vilela
author_facet Mendes, R. Vilela
Mendes, Hugo C.
Araújo, Tanya
author_role author
author2 Mendes, Hugo C.
Araújo, Tanya
author2_role author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Mendes, R. Vilela
Mendes, Hugo C.
Araújo, Tanya
dc.subject.por.fl_str_mv Network Signals
Graph-Transforms
Tomograms
Dynamics on Networks
topic Network Signals
Graph-Transforms
Tomograms
Dynamics on Networks
description Development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presen
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
2023-11-21T11:38:14Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/29455
url http://hdl.handle.net/10400.5/29455
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mendes, R. Vilela; Hugo C. Mendes and Tanya Araújo. (2016). ”Signals on graphs: transforms and tomograms”. Physica A: Statistical Mechanics and its Applications, Volume 50 .(Search PDF in 2023).
0378-4371
dx.doi.org/10.1016/j.physa.2016.01.002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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