Variational Bayesian Inference for Tensor Robust Principal Component Analysis
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909990035390464 |
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| author | Wang, Chao Zheng, Huiwen Chan, Raymond Wen, Youwei |
| author_facet | Wang, Chao Zheng, Huiwen Chan, Raymond Wen, Youwei |
| contents | Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Bayesian Inference for Tensor Robust Principal Component Analysis Wang, Chao Zheng, Huiwen Chan, Raymond Wen, Youwei Numerical Analysis Machine Learning Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches. |
| title | Variational Bayesian Inference for Tensor Robust Principal Component Analysis |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2412.18717 |