Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913807573450752 |
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| author | Xu, Yangyang Li, Kexin Yang, Li Wen, You-Wei |
| author_facet | Xu, Yangyang Li, Kexin Yang, Li Wen, You-Wei |
| contents | Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation Xu, Yangyang Li, Kexin Yang, Li Wen, You-Wei Numerical Analysis Computer Vision and Pattern Recognition Machine Learning 65K10, 15A69 I.4.5; G.1.6 Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods. |
| title | Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation |
| topic | Numerical Analysis Computer Vision and Pattern Recognition Machine Learning 65K10, 15A69 I.4.5; G.1.6 |
| url | https://arxiv.org/abs/2504.18323 |