Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method

Autores
Zhao, Qibin; Caiafa, Cesar Federico; Mandic, Danilo P.; Chao, Zenas C.; Nagasaka, Yasuo; Fujii, Naotaka; Zhang, Liqing; Cichocki, Andrzej
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.
Fil: Zhao, Qibin . RIKEN Brain Science Institute; Japón
Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); Argentina
Fil: Mandic, Danilo P. . Imperial College Of Science And Technology; Reino Unido
Fil: Chao, Zenas C. . RIKEN Brain Science Institute; Japón
Fil: Nagasaka, Yasuo . RIKEN Brain Science Institute; Japón
Fil: Fujii, Naotaka. RIKEN Brain Science Institute; Japón
Fil: Zhang, Liqing. Shanghai Jiao Tong University; China
Fil: Cichocki, Andrzej. RIKEN Brain Science Institute; Japón
Materia
Multilinear regression
Partial Least squares
Higher-order singular value decompostion
Constrained block Tucker decomposition
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:11336/4630
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/4630
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression methodZhao, Qibin Caiafa, Cesar FedericoMandic, Danilo P. Chao, Zenas C. Nagasaka, Yasuo Fujii, NaotakaZhang, LiqingCichocki, AndrzejMultilinear regressionPartial Least squaresHigher-order singular value decompostionConstrained block Tucker decompositionhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.Fil: Zhao, Qibin . RIKEN Brain Science Institute; JapónFil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Mandic, Danilo P. . Imperial College Of Science And Technology; Reino UnidoFil: Chao, Zenas C. . RIKEN Brain Science Institute; JapónFil: Nagasaka, Yasuo . RIKEN Brain Science Institute; JapónFil: Fujii, Naotaka. RIKEN Brain Science Institute; JapónFil: Zhang, Liqing. Shanghai Jiao Tong University; ChinaFil: Cichocki, Andrzej. RIKEN Brain Science Institute; JapónIEEE Computer Society2013-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/4630Zhao, Qibin ; Caiafa, Cesar Federico; Mandic, Danilo P. ; Chao, Zenas C. ; Nagasaka, Yasuo ; et al.; Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method; IEEE Computer Society; IEEE Transactions on Pattern Analysis and Machine Intelligence; 35; 7; 7-2013; 1660-16730162-8828enginfo:eu-repo/semantics/altIdentifier/doi/10.1109/TPAMI.2012.254info:eu-repo/semantics/altIdentifier/arxiv/http://arxiv.org/abs/1207.1230info:eu-repo/semantics/altIdentifier/url/https://www.computer.org/csdl/trans/tp/2013/07/ttp2013071660-abs.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:16Zoai:ri.conicet.gov.ar:11336/4630instacron: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:34982025-09-03 09:57:16.322CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
title Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
spellingShingle Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
Zhao, Qibin
Multilinear regression
Partial Least squares
Higher-order singular value decompostion
Constrained block Tucker decomposition
title_short Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
title_full Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
title_fullStr Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
title_full_unstemmed Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
title_sort Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method
dc.creator.none.fl_str_mv Zhao, Qibin
Caiafa, Cesar Federico
Mandic, Danilo P.
Chao, Zenas C.
Nagasaka, Yasuo
Fujii, Naotaka
Zhang, Liqing
Cichocki, Andrzej
author Zhao, Qibin
author_facet Zhao, Qibin
Caiafa, Cesar Federico
Mandic, Danilo P.
Chao, Zenas C.
Nagasaka, Yasuo
Fujii, Naotaka
Zhang, Liqing
Cichocki, Andrzej
author_role author
author2 Caiafa, Cesar Federico
Mandic, Danilo P.
Chao, Zenas C.
Nagasaka, Yasuo
Fujii, Naotaka
Zhang, Liqing
Cichocki, Andrzej
author2_role author
author
author
author
author
author
author
dc.subject.none.fl_str_mv Multilinear regression
Partial Least squares
Higher-order singular value decompostion
Constrained block Tucker decomposition
topic Multilinear regression
Partial Least squares
Higher-order singular value decompostion
Constrained block Tucker decomposition
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 new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.
Fil: Zhao, Qibin . RIKEN Brain Science Institute; Japón
Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); Argentina
Fil: Mandic, Danilo P. . Imperial College Of Science And Technology; Reino Unido
Fil: Chao, Zenas C. . RIKEN Brain Science Institute; Japón
Fil: Nagasaka, Yasuo . RIKEN Brain Science Institute; Japón
Fil: Fujii, Naotaka. RIKEN Brain Science Institute; Japón
Fil: Zhang, Liqing. Shanghai Jiao Tong University; China
Fil: Cichocki, Andrzej. RIKEN Brain Science Institute; Japón
description A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.
publishDate 2013
dc.date.none.fl_str_mv 2013-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/4630
Zhao, Qibin ; Caiafa, Cesar Federico; Mandic, Danilo P. ; Chao, Zenas C. ; Nagasaka, Yasuo ; et al.; Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method; IEEE Computer Society; IEEE Transactions on Pattern Analysis and Machine Intelligence; 35; 7; 7-2013; 1660-1673
0162-8828
url http://hdl.handle.net/11336/4630
identifier_str_mv Zhao, Qibin ; Caiafa, Cesar Federico; Mandic, Danilo P. ; Chao, Zenas C. ; Nagasaka, Yasuo ; et al.; Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method; IEEE Computer Society; IEEE Transactions on Pattern Analysis and Machine Intelligence; 35; 7; 7-2013; 1660-1673
0162-8828
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1109/TPAMI.2012.254
info:eu-repo/semantics/altIdentifier/arxiv/http://arxiv.org/abs/1207.1230
info:eu-repo/semantics/altIdentifier/url/https://www.computer.org/csdl/trans/tp/2013/07/ttp2013071660-abs.html
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
application/pdf
dc.publisher.none.fl_str_mv IEEE Computer Society
publisher.none.fl_str_mv IEEE Computer Society
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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score 13.13397

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