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Practical sketching algorithms for low-rank tucker approximation of large tensors

Practical sketching algorithms for low-rank tucker approximation of large tensors
Practical sketching algorithms for low-rank tucker approximation of large tensors
Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data compression and dimensionality reduction technique applied to the low-rank approximation of large matrices. This paper presents two practical randomized algorithms for low-rank Tucker approximation of large tensors based on sketching and power scheme, with a rigorous error-bound analysis. Numerical experiments on synthetic and real-world tensor data demonstrate the competitive performance of the proposed algorithms.
High-dimensional data, Randomized algorithm, Subspace power iteration, Tensor sketching, Tucker decomposition
1573-7691
Dong, Wandi
56863911-8254-4ca5-8f69-2d68b71aa68c
Yu, Gaohang
304aa1da-05ff-48d0-a19d-1e3a74de273b
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Dong, Wandi
56863911-8254-4ca5-8f69-2d68b71aa68c
Yu, Gaohang
304aa1da-05ff-48d0-a19d-1e3a74de273b
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee

Dong, Wandi, Yu, Gaohang, Qi, Liqun and Cai, Xiaohao (2023) Practical sketching algorithms for low-rank tucker approximation of large tensors. Journal of Scientific Computing, 95 (2), [52]. (doi:10.1007/s10915-023-02172-y).

Record type: Article

Abstract

Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data compression and dimensionality reduction technique applied to the low-rank approximation of large matrices. This paper presents two practical randomized algorithms for low-rank Tucker approximation of large tensors based on sketching and power scheme, with a rigorous error-bound analysis. Numerical experiments on synthetic and real-world tensor data demonstrate the competitive performance of the proposed algorithms.

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Practical Sketching Algorithms for Low Rank Tucker Approximation of Large Tensors - Accepted Manuscript
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More information

Accepted/In Press date: 28 February 2023
e-pub ahead of print date: 29 March 2023
Published date: 29 March 2023
Additional Information: Funding Information: G. Yu’s work was supported in part by the National Natural Science Foundation of China (No. 12071104) and the Natural Science Foundation of Zhejiang Province (No. LD19A010002). Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: High-dimensional data, Randomized algorithm, Subspace power iteration, Tensor sketching, Tucker decomposition

Identifiers

Local EPrints ID: 476912
URI: http://eprints.soton.ac.uk/id/eprint/476912
ISSN: 1573-7691
PURE UUID: 9b9337a3-b261-4b63-8a53-9e394123d938
ORCID for Xiaohao Cai: ORCID iD orcid.org/0000-0003-0924-2834

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Date deposited: 19 May 2023 16:34
Last modified: 17 Mar 2024 07:45

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Contributors

Author: Wandi Dong
Author: Gaohang Yu
Author: Liqun Qi
Author: Xiaohao Cai ORCID iD

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