LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911093588230144 |
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| author | Gong, Wenwu Yang, Lili |
| author_facet | Gong, Wenwu Yang, Lili |
| contents | Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank approximations or local smoothness regularization, but each suffers from notable limitations: low-rank methods are computationally expensive and may disrupt intrinsic data structures, while smoothness-based approaches often require extensive manual parameter tuning and exhibit poor generalization. In this paper, we propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior modeling within a Tucker decomposition. Specifically, LRTuckerRep encodes low rankness through a self-adaptive weighted nuclear norm on the factor matrices and a sparse Tucker core, while capturing smoothness via a parameter-free Laplacian-based regularization on the factor spaces. To efficiently solve the resulting nonconvex optimization problem, we develop two iterative algorithms with provable convergence guarantees. Extensive experiments on multi-dimensional image inpainting and traffic data imputation demonstrate that LRTuckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion Gong, Wenwu Yang, Lili Machine Learning Computer Vision and Pattern Recognition Numerical Analysis Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank approximations or local smoothness regularization, but each suffers from notable limitations: low-rank methods are computationally expensive and may disrupt intrinsic data structures, while smoothness-based approaches often require extensive manual parameter tuning and exhibit poor generalization. In this paper, we propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior modeling within a Tucker decomposition. Specifically, LRTuckerRep encodes low rankness through a self-adaptive weighted nuclear norm on the factor matrices and a sparse Tucker core, while capturing smoothness via a parameter-free Laplacian-based regularization on the factor spaces. To efficiently solve the resulting nonconvex optimization problem, we develop two iterative algorithms with provable convergence guarantees. Extensive experiments on multi-dimensional image inpainting and traffic data imputation demonstrate that LRTuckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines. |
| title | LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion |
| topic | Machine Learning Computer Vision and Pattern Recognition Numerical Analysis |
| url | https://arxiv.org/abs/2508.03755 |