Iterative hard thresholding for low CP-rank tensor models
Iterative hard thresholding for low CP-rank tensor models
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DOI：
10.1080/03081087.2021.1992335
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发表时间：
2019-08
影响因子：
1.1
通讯作者：
Rachel Grotheer;S. Li;A. Ma;D. Needell;Jing Qin
中科院分区：
文献类型：
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作者：
Rachel Grotheer;S. Li;A. Ma;D. Needell;Jing Qin
从少量的线性测量中恢复低秩矩阵现在已知可以在测量的各种模型假设下实现。这些结果显示了稳健性，并有可证明的理论保证。然而，张量恢复的扩展直到最近才开始研究和发展，尽管有大量的实际张量应用。最近，提出了一种迭代硬阈值法的张量变体，并获得了精确保证低塔克秩张量恢复的理论结果。在本文中，我们利用并证明了限制等距性质（RIP）的一个类似张量版本，将这些结果推广到低CANDECOMP/PARAFAC （CP）秩张量。在这样做的过程中，我们利用了最近对CP分解的有效近似的结果，消除了对先前工作中具有挑战性的假设的需要。我们用实证结果补充了我们的理论发现，展示了该方法的潜力。
Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, extensions to tensor recovery have only recently began to be studied and developed, despite an abundance of practical tensor applications. Recently, a tensor variant of the Iterative Hard Thresholding method was proposed and theoretical results were obtained that exact guarantee recovery of tensors with low Tucker rank. In this paper, we utilize and prove a similar tensor version of the Restricted Isometry Property (RIP) to extend these results for tensors with low CANDECOMP/PARAFAC (CP) rank. In doing so, we leverage recent results on efficient approximations of CP decompositions that remove the need for challenging assumptions in prior works. We complement our theoretical findings with empirical results that showcase the potential of the approach.