Learning unbalanced and sparse low-order tensors
Learning unbalanced and sparse low-order tensors
Efficient techniques are developed for completing unbalanced and sparse low-order tensors, which cannot be effectively completed by popular matrix-rank optimization based techniques such as compressed sensing and/or the ℓq-matrix-metric. We use our previously developed 2D-index encoding technique for tensor augmentation in order to represent these incomplete low-order tensors by high-order but low-dimensional tensors with their modes building up a coarse-grained hierachy of correlations among the incomplete tensor entries. The concept of tensor-trains is then exploited for decomposing these augmented tensors into trains of balanced and sparse matrices for efficient completion. More explicitly, we develop powerful algorithms exhibiting an excellent performance vs. complexity trade-off, which are supported by numerical examples by relying on matrix data and third-order tensor data derived from color image pixels.
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5624-5638
Hoang, P.
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Tuan, H.
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Son, T.
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Poor, H. Vincent
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Hanzo, Lajos
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14 November 2022
Hoang, P.
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Tuan, H.
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Son, T.
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Poor, H. Vincent
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Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Hoang, P., Tuan, H., Son, T., Poor, H. Vincent and Hanzo, Lajos
(2022)
Learning unbalanced and sparse low-order tensors.
IEEE Trans. on Signal Processing, 70, .
(doi:10.1109/TSP.2022.3221661).
Abstract
Efficient techniques are developed for completing unbalanced and sparse low-order tensors, which cannot be effectively completed by popular matrix-rank optimization based techniques such as compressed sensing and/or the ℓq-matrix-metric. We use our previously developed 2D-index encoding technique for tensor augmentation in order to represent these incomplete low-order tensors by high-order but low-dimensional tensors with their modes building up a coarse-grained hierachy of correlations among the incomplete tensor entries. The concept of tensor-trains is then exploited for decomposing these augmented tensors into trains of balanced and sparse matrices for efficient completion. More explicitly, we develop powerful algorithms exhibiting an excellent performance vs. complexity trade-off, which are supported by numerical examples by relying on matrix data and third-order tensor data derived from color image pixels.
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Learning Unbalanced and Sparse Low-Order Tensors
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Learning_Unbalanced_and_Sparse_Low-Order_Tensors
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Accepted/In Press date: 8 November 2022
Published date: 14 November 2022
Additional Information:
Funding Information:
This work was supported in part by Australian Research Council Discovery Projects under Grant DP190102501, in part by U.S. National Science Foundation under Grant CCF-1908308, in part by the C3.ai Digital Transformation Institute, in part by the UK Engineering and Physical Sciences Research Council under Grants EP/W016605/1 and EP/P003990/1 (COALESCE), and in part by European Research Council Advanced Fellow Grant QuantCom under Grant 789028.
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© 2022 IEEE.
Keywords:
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Identifiers
Local EPrints ID: 472444
URI: http://eprints.soton.ac.uk/id/eprint/472444
PURE UUID: 3e8cc729-40b2-4023-b1cb-208609b2823b
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Date deposited: 05 Dec 2022 18:07
Last modified: 18 Mar 2024 02:36
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Contributors
Author:
P. Hoang
Author:
H. Tuan
Author:
T. Son
Author:
H. Vincent Poor
Author:
Lajos Hanzo
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