Incremental algorithms for truncated higher-order singular value decompositions

Chao Zeng; Michael K. Ng; Tai Xiang Jiang

doi:10.1007/s10543-023-01004-7

Incremental algorithms for truncated higher-order singular value decompositions

Chao Zeng, Michael K. Ng, Tai Xiang Jiang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not only the factor matrices but also the core tensor are updated in an incremental style. The costs of these algorithms are compared and the approximation errors are analyzed. Numerical results demonstrate that the proposed incremental algorithms have advantages in online computation.

Original language	English
Article number	4
Number of pages	28
Journal	BIT Numerical Mathematics
Volume	64
Issue number	1
Early online date	8 Jan 2024
DOIs	https://doi.org/10.1007/s10543-023-01004-7
Publication status	Published - Mar 2024

Scopus Subject Areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Incremental algorithm
SVD updating
Truncated higher-order singular value decomposition

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10.1007/s10543-023-01004-7

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title = "Incremental algorithms for truncated higher-order singular value decompositions",

abstract = "We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not only the factor matrices but also the core tensor are updated in an incremental style. The costs of these algorithms are compared and the approximation errors are analyzed. Numerical results demonstrate that the proposed incremental algorithms have advantages in online computation.",

keywords = "Incremental algorithm, SVD updating, Truncated higher-order singular value decomposition",

author = "Chao Zeng and Ng, {Michael K.} and Jiang, {Tai Xiang}",

note = "Funding information: Chao Zeng{\textquoteright}s work was supported in part by the National Natural Science Foundation of China (12201319) and the Fundamental Research Funds for the Central Universities, Nankai University (63231142). Michael K. Ng{\textquoteright}s research supported in part by the HKRGC GRF 17201020 and 17300021, and CRF C7004-21GF, and Joint NSFC and RGC NHKU769/21. Tai-Xiang Jiang{\textquoteright}s work was supported in part by the National Natural Science Foundation of China (12001446), Natural Science Foundation of Sichuan, China (2022NSFSC1798), the Fundamental Research Funds for the Central Universities, and the Guanghua Talent Project. Publisher Copyright: {\textcopyright} 2024, The Author(s), under exclusive licence to Springer Nature B.V.",

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doi = "10.1007/s10543-023-01004-7",

language = "English",

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AU - Ng, Michael K.

AU - Jiang, Tai Xiang

N1 - Funding information: Chao Zeng’s work was supported in part by the National Natural Science Foundation of China (12201319) and the Fundamental Research Funds for the Central Universities, Nankai University (63231142). Michael K. Ng’s research supported in part by the HKRGC GRF 17201020 and 17300021, and CRF C7004-21GF, and Joint NSFC and RGC NHKU769/21. Tai-Xiang Jiang’s work was supported in part by the National Natural Science Foundation of China (12001446), Natural Science Foundation of Sichuan, China (2022NSFSC1798), the Fundamental Research Funds for the Central Universities, and the Guanghua Talent Project. Publisher Copyright: © 2024, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2024/3

Y1 - 2024/3

N2 - We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not only the factor matrices but also the core tensor are updated in an incremental style. The costs of these algorithms are compared and the approximation errors are analyzed. Numerical results demonstrate that the proposed incremental algorithms have advantages in online computation.

AB - We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not only the factor matrices but also the core tensor are updated in an incremental style. The costs of these algorithms are compared and the approximation errors are analyzed. Numerical results demonstrate that the proposed incremental algorithms have advantages in online computation.

KW - Incremental algorithm

KW - SVD updating

KW - Truncated higher-order singular value decomposition

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U2 - 10.1007/s10543-023-01004-7

DO - 10.1007/s10543-023-01004-7

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JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

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ER -

Incremental algorithms for truncated higher-order singular value decompositions

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