Multilinear subspace regression: an orthogonal tensor decomposition approach

Autores
Zhao, Qibin; Caiafa, César Federico; Mandic, Danilo P.; Zhang, Liqing; Ball, Tonio; Schulze Bonhage, Andreas; Cichocki, Andrzej
Año de publicación
2011
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).
Fil: Zhao, Qibin. Riken. Brain Science Institute; Japón
Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina
Fil: Mandic, Danilo P.. Imperial College Of Science And Technology; Reino Unido
Fil: Zhang, Liqing. Shanghai Jiao Tong University; China
Fil: Ball, Tonio. University Of Freiburg; Alemania
Fil: Schulze Bonhage, Andreas. University Of Freidburg; Alemania
Fil: Cichocki, Andrzej. Riken. Brain Science Institute; Japón
25th Annual Conference on Neural Information Processing Systems
Granada
España
Neural Information Processing Systems Foundation
Materia
Tensor network
Linear Regression
EEG
EcoG
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/225339
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Multilinear subspace regression: an orthogonal tensor decomposition approachZhao, QibinCaiafa, César FedericoMandic, Danilo P.Zhang, LiqingBall, TonioSchulze Bonhage, AndreasCichocki, AndrzejTensor networkLinear RegressionEEGEcoGhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).Fil: Zhao, Qibin. Riken. Brain Science Institute; JapónFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Mandic, Danilo P.. Imperial College Of Science And Technology; Reino UnidoFil: Zhang, Liqing. Shanghai Jiao Tong University; ChinaFil: Ball, Tonio. University Of Freiburg; AlemaniaFil: Schulze Bonhage, Andreas. University Of Freidburg; AlemaniaFil: Cichocki, Andrzej. Riken. Brain Science Institute; Japón25th Annual Conference on Neural Information Processing SystemsGranadaEspañaNeural Information Processing Systems FoundationCurran Associates Inc.2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectConferenciaBookhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/225339Multilinear subspace regression: an orthogonal tensor decomposition approach; 25th Annual Conference on Neural Information Processing Systems; Granada; España; 2011; 1-99781618395993CONICET DigitalCONICETenghttps://nips.cc/Conferences/2011info:eu-repo/semantics/altIdentifier/url/https://proceedings.neurips.cc/paper_files/paper/2011/file/1343777b8ead1cef5a79b78a1a48d805-Paper.pdfinfo:eu-repo/semantics/altIdentifier/url/https://dl.acm.org/doi/10.5555/2986459.2986601info:eu-repo/semantics/altIdentifier/url/https://dl.acm.org/doi/proceedings/10.5555/2986459Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:23:22Zoai:ri.conicet.gov.ar:11336/225339instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:23:22.928CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multilinear subspace regression: an orthogonal tensor decomposition approach
title Multilinear subspace regression: an orthogonal tensor decomposition approach
spellingShingle Multilinear subspace regression: an orthogonal tensor decomposition approach
Zhao, Qibin
Tensor network
Linear Regression
EEG
EcoG
title_short Multilinear subspace regression: an orthogonal tensor decomposition approach
title_full Multilinear subspace regression: an orthogonal tensor decomposition approach
title_fullStr Multilinear subspace regression: an orthogonal tensor decomposition approach
title_full_unstemmed Multilinear subspace regression: an orthogonal tensor decomposition approach
title_sort Multilinear subspace regression: an orthogonal tensor decomposition approach
dc.creator.none.fl_str_mv Zhao, Qibin
Caiafa, César Federico
Mandic, Danilo P.
Zhang, Liqing
Ball, Tonio
Schulze Bonhage, Andreas
Cichocki, Andrzej
author Zhao, Qibin
author_facet Zhao, Qibin
Caiafa, César Federico
Mandic, Danilo P.
Zhang, Liqing
Ball, Tonio
Schulze Bonhage, Andreas
Cichocki, Andrzej
author_role author
author2 Caiafa, César Federico
Mandic, Danilo P.
Zhang, Liqing
Ball, Tonio
Schulze Bonhage, Andreas
Cichocki, Andrzej
author2_role author
author
author
author
author
author
dc.subject.none.fl_str_mv Tensor network
Linear Regression
EEG
EcoG
topic Tensor network
Linear Regression
EEG
EcoG
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).
Fil: Zhao, Qibin. Riken. Brain Science Institute; Japón
Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina
Fil: Mandic, Danilo P.. Imperial College Of Science And Technology; Reino Unido
Fil: Zhang, Liqing. Shanghai Jiao Tong University; China
Fil: Ball, Tonio. University Of Freiburg; Alemania
Fil: Schulze Bonhage, Andreas. University Of Freidburg; Alemania
Fil: Cichocki, Andrzej. Riken. Brain Science Institute; Japón
25th Annual Conference on Neural Information Processing Systems
Granada
España
Neural Information Processing Systems Foundation
description A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Conferencia
Book
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/225339
Multilinear subspace regression: an orthogonal tensor decomposition approach; 25th Annual Conference on Neural Information Processing Systems; Granada; España; 2011; 1-9
9781618395993
CONICET Digital
CONICET
url http://hdl.handle.net/11336/225339
identifier_str_mv Multilinear subspace regression: an orthogonal tensor decomposition approach; 25th Annual Conference on Neural Information Processing Systems; Granada; España; 2011; 1-9
9781618395993
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://nips.cc/Conferences/2011
info:eu-repo/semantics/altIdentifier/url/https://proceedings.neurips.cc/paper_files/paper/2011/file/1343777b8ead1cef5a79b78a1a48d805-Paper.pdf
info:eu-repo/semantics/altIdentifier/url/https://dl.acm.org/doi/10.5555/2986459.2986601
info:eu-repo/semantics/altIdentifier/url/https://dl.acm.org/doi/proceedings/10.5555/2986459
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Curran Associates Inc.
publisher.none.fl_str_mv Curran Associates Inc.
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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