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arXiv · 1207.5326

Guarantees of Augmented Trace Norm Models in Tensor Recovery

Ziqiang Shi·Jiqing Han·Tieran Zheng·Shiwen Deng·Ji Li
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Abstract

This paper studies the recovery guarantees of the models of minimizing $\|\mathcal{X}\|_*+\frac{1}{2\alpha}\|\mathcal{X}\|_F^2$ where $\mathcal{X}$ is a tensor and $\|\mathcal{X}\|_*$ and $\|\mathcal{X}\|_F$ are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing $\|\mathcal{X}\|_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor $\mathcal{X}^0$, minimizing $\|\mathcal{X}\|_*+\frac{1}{2\alpha}\|\mathcal{X}\|_F^2$ returns the same solution as minimizing $\|\mathcal{X}\|_*$ almost whenever $\alpha\geq10\mathop {\max}\limits_{i}\|X^0_{(i)}\|_2$.

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Ziqiang Shi, Jiqing Han, Tieran Zheng, Shiwen Deng, Ji Li. 2012-07-23. Guarantees of Augmented Trace Norm Models in Tensor Recovery. https://arxiv.org/abs/1207.5326

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