A new algorithm by embedding structured data for low-rank tensor ring completion
In this paper, we put up with a new algorithm for tensor completion problems that include missing slices or row/column fibers, where embedding a structured tensor by a multi-way delay-embedding transform (MDT) makes the tensor to be completed have a special structure. The main idea is to employ a te...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025297 |
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| author | Ruiping Wen Tingyan Liu Yalei Pei |
| author_facet | Ruiping Wen Tingyan Liu Yalei Pei |
| author_sort | Ruiping Wen |
| collection | DOAJ |
| description | In this paper, we put up with a new algorithm for tensor completion problems that include missing slices or row/column fibers, where embedding a structured tensor by a multi-way delay-embedding transform (MDT) makes the tensor to be completed have a special structure. The main idea is to employ a tensor completion algorithm based on the tensor ring rank, constructing latent tensor ring factors with a structure that approximates the original tensor starting from the tensor structure. It is also proved that the sequence generated by the new algorithm converges to the optimal solution. Finally, the feasibility of the proposed algorithm is verified by experiments. Compared with other completed algorithms based on tensor ring rank, the completed accuracy is improved, up to 30%. |
| format | Article |
| id | doaj-art-0df0d551ef91499d86fed3fdfd816ba2 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-0df0d551ef91499d86fed3fdfd816ba22025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-03-011036492651110.3934/math.2025297A new algorithm by embedding structured data for low-rank tensor ring completionRuiping Wen0Tingyan Liu1Yalei Pei2Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Taiyuan Normal University, Jinzhong 030619, Shanxi, ChinaSchool of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, Shanxi, ChinaSchool of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, Shanxi, ChinaIn this paper, we put up with a new algorithm for tensor completion problems that include missing slices or row/column fibers, where embedding a structured tensor by a multi-way delay-embedding transform (MDT) makes the tensor to be completed have a special structure. The main idea is to employ a tensor completion algorithm based on the tensor ring rank, constructing latent tensor ring factors with a structure that approximates the original tensor starting from the tensor structure. It is also proved that the sequence generated by the new algorithm converges to the optimal solution. Finally, the feasibility of the proposed algorithm is verified by experiments. Compared with other completed algorithms based on tensor ring rank, the completed accuracy is improved, up to 30%.https://www.aimspress.com/article/doi/10.3934/math.2025297low-rank tensor completiontensor ring decompositionembedded spacestructured data |
| spellingShingle | Ruiping Wen Tingyan Liu Yalei Pei A new algorithm by embedding structured data for low-rank tensor ring completion AIMS Mathematics low-rank tensor completion tensor ring decomposition embedded space structured data |
| title | A new algorithm by embedding structured data for low-rank tensor ring completion |
| title_full | A new algorithm by embedding structured data for low-rank tensor ring completion |
| title_fullStr | A new algorithm by embedding structured data for low-rank tensor ring completion |
| title_full_unstemmed | A new algorithm by embedding structured data for low-rank tensor ring completion |
| title_short | A new algorithm by embedding structured data for low-rank tensor ring completion |
| title_sort | new algorithm by embedding structured data for low rank tensor ring completion |
| topic | low-rank tensor completion tensor ring decomposition embedded space structured data |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025297 |
| work_keys_str_mv | AT ruipingwen anewalgorithmbyembeddingstructureddataforlowranktensorringcompletion AT tingyanliu anewalgorithmbyembeddingstructureddataforlowranktensorringcompletion AT yaleipei anewalgorithmbyembeddingstructureddataforlowranktensorringcompletion AT ruipingwen newalgorithmbyembeddingstructureddataforlowranktensorringcompletion AT tingyanliu newalgorithmbyembeddingstructureddataforlowranktensorringcompletion AT yaleipei newalgorithmbyembeddingstructureddataforlowranktensorringcompletion |