Robust Completion for Rank-1 Tensors with Noises
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916668514500608 |
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| author | Nie, Jiawang Tang, Xindong Zhou, Jinling |
| author_facet | Nie, Jiawang Tang, Xindong Zhou, Jinling |
| contents | This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the observed tensor is sufficiently close to be rank-1, we show that this biquadratic optimization produces an accurate rank-1 tensor completion. Second, we give an efficient convex relaxation for solving the biquadratic optimization. When the optimizer matrix is separable, we show how to get optimizers for the biquadratic optimization and how to compute the rank-1 completing tensor. When that matrix is not separable, we apply its spectral decomposition to obtain an approximate rank-1 completing tensor. Numerical experiments are given to explore the efficiency of this biquadratic optimization model and the proposed convex relaxation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Completion for Rank-1 Tensors with Noises Nie, Jiawang Tang, Xindong Zhou, Jinling Optimization and Control 15A69, 90C23, 65F99 This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the observed tensor is sufficiently close to be rank-1, we show that this biquadratic optimization produces an accurate rank-1 tensor completion. Second, we give an efficient convex relaxation for solving the biquadratic optimization. When the optimizer matrix is separable, we show how to get optimizers for the biquadratic optimization and how to compute the rank-1 completing tensor. When that matrix is not separable, we apply its spectral decomposition to obtain an approximate rank-1 completing tensor. Numerical experiments are given to explore the efficiency of this biquadratic optimization model and the proposed convex relaxation. |
| title | Robust Completion for Rank-1 Tensors with Noises |
| topic | Optimization and Control 15A69, 90C23, 65F99 |
| url | https://arxiv.org/abs/2504.00398 |