A new algorithm by embedding structured data for low-rank tensor ring completion

Ruiping Wen; Tingyan Liu; Yalei Pei; Ruiping Wen; Tingyan Liu; Yalei Pei

doi:10.3934/math.2025297

AIMS Mathematics

2025, Volume 10, Issue 3: 6492-6511. doi: 10.3934/math.2025297

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Research article

A new algorithm by embedding structured data for low-rank tensor ring completion

1.
Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Taiyuan Normal University, Jinzhong 030619, Shanxi, China
2.
School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, Shanxi, China

Received: 28 September 2024 Revised: 05 March 2025 Accepted: 14 March 2025 Published: 24 March 2025
MSC : 15A69, 90C06, 90C47

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%.
- low-rank tensor completion,
- tensor ring decomposition,
- embedded space,
- structured data
Citation: Ruiping Wen, Tingyan Liu, Yalei Pei. A new algorithm by embedding structured data for low-rank tensor ring completion[J]. AIMS Mathematics, 2025, 10(3): 6492-6511. doi: 10.3934/math.2025297

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Abstract

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%.

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