Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

Autores
Ahmadi Asl, Salman; Caiafa, César Federico; Cichocki, Andrzej; Phan, Anh Huy; Tanaka, Toshihisa; Oseledets, Ivan; Wang, Jun
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends stateof-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations.We discuss several possible generalizations of the CMA to tensors, including CTAs: based on  ber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.
Fil: Ahmadi Asl, Salman. Skoltech - Skolkovo Institute Of Science And Technology; Rusia
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: Cichocki, Andrzej. Skolkovo Institute of Science and Technology; Rusia
Fil: Phan, Anh Huy. Skolkovo Institute of Science and Technology; Rusia
Fil: Tanaka, Toshihisa. Agricultural University Of Tokyo; Japón
Fil: Oseledets, Ivan. Skolkovo Institute of Science and Technology; Rusia
Fil: Wang, Jun. Skolkovo Institute of Science and Technology; Rusia
Materia
CUR algorithms
cross approximations
tensor decomposition
randomization
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:11336/149081
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Cross Tensor Approximation Methods for Compression and Dimensionality ReductionAhmadi Asl, SalmanCaiafa, César FedericoCichocki, AndrzejPhan, Anh HuyTanaka, ToshihisaOseledets, IvanWang, JunCUR algorithmscross approximationstensor decompositionrandomizationhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends stateof-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations.We discuss several possible generalizations of the CMA to tensors, including CTAs: based on  ber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.Fil: Ahmadi Asl, Salman. Skoltech - Skolkovo Institute Of Science And Technology; RusiaFil: 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: Cichocki, Andrzej. Skolkovo Institute of Science and Technology; RusiaFil: Phan, Anh Huy. Skolkovo Institute of Science and Technology; RusiaFil: Tanaka, Toshihisa. Agricultural University Of Tokyo; JapónFil: Oseledets, Ivan. Skolkovo Institute of Science and Technology; RusiaFil: Wang, Jun. Skolkovo Institute of Science and Technology; RusiaIEEE2021-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/149081Ahmadi Asl, Salman; Caiafa, César Federico; Cichocki, Andrzej; Phan, Anh Huy; Tanaka, Toshihisa; et al.; Cross Tensor Approximation Methods for Compression and Dimensionality Reduction; IEEE; IEEE Access; 9; 11-2021; 150809-1508382169-35362169-3536CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/9599673?source=authoralertinfo:eu-repo/semantics/altIdentifier/doi/10.1109/ACCESS.2021.3125069info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:42:03Zoai:ri.conicet.gov.ar:11336/149081instacron: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 14:42:03.502CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
spellingShingle Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
Ahmadi Asl, Salman
CUR algorithms
cross approximations
tensor decomposition
randomization
title_short Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_full Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_fullStr Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_full_unstemmed Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_sort Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
dc.creator.none.fl_str_mv Ahmadi Asl, Salman
Caiafa, César Federico
Cichocki, Andrzej
Phan, Anh Huy
Tanaka, Toshihisa
Oseledets, Ivan
Wang, Jun
author Ahmadi Asl, Salman
author_facet Ahmadi Asl, Salman
Caiafa, César Federico
Cichocki, Andrzej
Phan, Anh Huy
Tanaka, Toshihisa
Oseledets, Ivan
Wang, Jun
author_role author
author2 Caiafa, César Federico
Cichocki, Andrzej
Phan, Anh Huy
Tanaka, Toshihisa
Oseledets, Ivan
Wang, Jun
author2_role author
author
author
author
author
author
dc.subject.none.fl_str_mv CUR algorithms
cross approximations
tensor decomposition
randomization
topic CUR algorithms
cross approximations
tensor decomposition
randomization
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends stateof-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations.We discuss several possible generalizations of the CMA to tensors, including CTAs: based on  ber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.
Fil: Ahmadi Asl, Salman. Skoltech - Skolkovo Institute Of Science And Technology; Rusia
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: Cichocki, Andrzej. Skolkovo Institute of Science and Technology; Rusia
Fil: Phan, Anh Huy. Skolkovo Institute of Science and Technology; Rusia
Fil: Tanaka, Toshihisa. Agricultural University Of Tokyo; Japón
Fil: Oseledets, Ivan. Skolkovo Institute of Science and Technology; Rusia
Fil: Wang, Jun. Skolkovo Institute of Science and Technology; Rusia
description Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends stateof-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations.We discuss several possible generalizations of the CMA to tensors, including CTAs: based on  ber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.
publishDate 2021
dc.date.none.fl_str_mv 2021-11
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/11336/149081
Ahmadi Asl, Salman; Caiafa, César Federico; Cichocki, Andrzej; Phan, Anh Huy; Tanaka, Toshihisa; et al.; Cross Tensor Approximation Methods for Compression and Dimensionality Reduction; IEEE; IEEE Access; 9; 11-2021; 150809-150838
2169-3536
2169-3536
CONICET Digital
CONICET
url http://hdl.handle.net/11336/149081
identifier_str_mv Ahmadi Asl, Salman; Caiafa, César Federico; Cichocki, Andrzej; Phan, Anh Huy; Tanaka, Toshihisa; et al.; Cross Tensor Approximation Methods for Compression and Dimensionality Reduction; IEEE; IEEE Access; 9; 11-2021; 150809-150838
2169-3536
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/9599673?source=authoralert
info:eu-repo/semantics/altIdentifier/doi/10.1109/ACCESS.2021.3125069
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.publisher.none.fl_str_mv IEEE
publisher.none.fl_str_mv IEEE
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
_version_ 1846082920494661632
score 13.22299

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