Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format
Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approxima...
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| Autor*in: |
Che, Maolin [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 194(2022), 3 vom: 24. Juni, Seite 852-877 |
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| Übergeordnetes Werk: |
volume:194 ; year:2022 ; number:3 ; day:24 ; month:06 ; pages:852-877 |
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| DOI / URN: |
10.1007/s10957-022-02051-w |
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OLC2079232886 |
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10.1007/s10957-022-02051-w doi (DE-627)OLC2079232886 (DE-He213)s10957-022-02051-w-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Che, Maolin verfasserin aut Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples. Tensor CUR decomposition Low multilinear rank approximation Maximal volume sub-matrices Mode- unfolding Tucker decomposition Chen, Juefei aut Wei, Yimin aut Enthalten in Journal of optimization theory and applications Springer US, 1967 194(2022), 3 vom: 24. Juni, Seite 852-877 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:194 year:2022 number:3 day:24 month:06 pages:852-877 https://doi.org/10.1007/s10957-022-02051-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 194 2022 3 24 06 852-877 |
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10.1007/s10957-022-02051-w doi (DE-627)OLC2079232886 (DE-He213)s10957-022-02051-w-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Che, Maolin verfasserin aut Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples. Tensor CUR decomposition Low multilinear rank approximation Maximal volume sub-matrices Mode- unfolding Tucker decomposition Chen, Juefei aut Wei, Yimin aut Enthalten in Journal of optimization theory and applications Springer US, 1967 194(2022), 3 vom: 24. Juni, Seite 852-877 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:194 year:2022 number:3 day:24 month:06 pages:852-877 https://doi.org/10.1007/s10957-022-02051-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 194 2022 3 24 06 852-877 |
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Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2079232886</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506042911.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10957-022-02051-w</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2079232886</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10957-022-02051-w-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">330</subfield><subfield code="a">510</subfield><subfield code="a">000</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 6420</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SA 6420</subfield><subfield code="q">VZ</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Che, Maolin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. 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