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
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
29 March 2023
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).
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.
Text
Practical Sketching Algorithms for Low Rank Tucker Approximation of Large Tensors
- Accepted Manuscript
Available under License Other.
More information
Accepted/In Press date: 28 February 2023
e-pub ahead of print date: 29 March 2023
Published date: 29 March 2023
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
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Date deposited: 19 May 2023 16:34
Last modified: 12 Jul 2024 04:07
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Contributors
Author:
Wandi Dong
Author:
Gaohang Yu
Author:
Liqun Qi
Author:
Xiaohao Cai
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