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One-bit tensor completion via transformed tensor singular value decomposition
Applied Mathematical Modelling ( IF 5 ) Pub Date : 2021-02-28 , DOI: 10.1016/j.apm.2021.02.032
Jingyao Hou , Feng Zhang , Jianjun Wang

This paper considers the problem of low-tubal-rank tensor completion from incomplete one-bit observations. Our work is inspired by the recently proposed invertible linear transforms based tensor-tensor product and transformed tensor singular value decomposition (t-SVD). Under this framework, a tensor nuclear norm constrained maximum log-likelihood estimation model is proposed, which is convex and efficiently solved. The feasibility of the model is proved with an upper bound of the estimation error obtained. We also show a lower bound of the worst-case estimation error, which combing with the obtained upper bound demonstrates that the estimation error is nearly order-optimal. Furthermore, an algorithm based on the alternating direction multipliers method (ADMM) and non-monotone spectral projected-gradient (SPG) method is designed to solve the estimation model. Simulations are performed to show the effectiveness of the proposed method, and the applications to real-world data demonstrate the promising performance of the proposed method.



中文翻译:

通过变换张量奇异值分解实现一位张量完成

本文从不完整的一位观测结果考虑了低管形张量完成的问题。我们的工作受到最近提出的基于张量-张量积的可逆线性变换和变换的张量奇异值分解(t-SVD)的启发。在此框架下,提出了一个张量核规范约束最大对数似然估计模型,该模型是凸的并且可以有效求解。所获得的估计误差的上限证明了该模型的可行性。我们还显示了最坏情况估计误差的下限,将其与获得的上限相结合,表明估计误差几乎是最优的。此外,设计了一种基于交变方向乘数法(ADMM)和非单调频谱投影梯度法(SPG)的算法来求解估计模型。仿真结果表明了该方法的有效性,并将其应用于现实世界的数据证明了该方法的良好前景。

更新日期:2021-02-28
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