A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery
In this paper, a new hybrid singular value thresholding with diagonal-modify algorithm based on the augmented Lagrange multiplier (ALM) method was proposed for low-rank matrix recovery, in which only part singular values were treated by a hybrid threshold operator with diagonal-update, and which all...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024274 |
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| _version_ | 1832590750855987200 |
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| author | Ruiping Wen Liang Zhang Yalei Pei |
| author_facet | Ruiping Wen Liang Zhang Yalei Pei |
| author_sort | Ruiping Wen |
| collection | DOAJ |
| description | In this paper, a new hybrid singular value thresholding with diagonal-modify algorithm based on the augmented Lagrange multiplier (ALM) method was proposed for low-rank matrix recovery, in which only part singular values were treated by a hybrid threshold operator with diagonal-update, and which allowed the algorithm to make use of simple arithmetic operation and keep the computational cost of each iteration low. The new algorithm decreased the complexity of the singular value decomposition and shortened the computing time. The convergence of the new algorithm was discussed. Finally, numerical experiments shown that the new algorithm greatly improved the solving efficiency of a matrix recovery problem and saved the calculation cost, and its effect was obviously better than that of the other algorithms mentioned in experiments. |
| format | Article |
| id | doaj-art-72975148875042b88f8e0818752d9c8f |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-72975148875042b88f8e0818752d9c8f2025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132115926594210.3934/era.2024274A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recoveryRuiping Wen0Liang Zhang1Yalei Pei2Shanxi Key Laboratory for Intelligent Optimization Computing and Block-chain Technology, Taiyuan Normal University, Jinzhong 030619, ChinaSchool of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, ChinaSchool of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, ChinaIn this paper, a new hybrid singular value thresholding with diagonal-modify algorithm based on the augmented Lagrange multiplier (ALM) method was proposed for low-rank matrix recovery, in which only part singular values were treated by a hybrid threshold operator with diagonal-update, and which allowed the algorithm to make use of simple arithmetic operation and keep the computational cost of each iteration low. The new algorithm decreased the complexity of the singular value decomposition and shortened the computing time. The convergence of the new algorithm was discussed. Finally, numerical experiments shown that the new algorithm greatly improved the solving efficiency of a matrix recovery problem and saved the calculation cost, and its effect was obviously better than that of the other algorithms mentioned in experiments.https://www.aimspress.com/article/doi/10.3934/era.2024274low-rank matrix recoveryaugmented lagrange multiplierdiagonal-modifyhybrid singular value threshold |
| spellingShingle | Ruiping Wen Liang Zhang Yalei Pei A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery Electronic Research Archive low-rank matrix recovery augmented lagrange multiplier diagonal-modify hybrid singular value threshold |
| title | A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery |
| title_full | A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery |
| title_fullStr | A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery |
| title_full_unstemmed | A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery |
| title_short | A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery |
| title_sort | hybrid singular value thresholding algorithm with diagonal modify for low rank matrix recovery |
| topic | low-rank matrix recovery augmented lagrange multiplier diagonal-modify hybrid singular value threshold |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024274 |
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