双因子张量范数正则化低秩张量填充
Double Factor Tensor Norm Regularized Low Rank Tensor Completion
DOI: 10.12677/AAM.2022.1110732, PDF,  被引量    科研立项经费支持
作者: 李鸿燕*：辽宁师范大学，辽宁 大连；姜 伟：辽宁师范大学，辽宁 大连；温州大学，浙江 温州
关键词: 低秩张量恢复；张量Schatten-p范数；分解；Recovery Problem of Low Rank Tensors； T-Schatten-p Norm； Decompose
摘要: 本文提出了一种新的正则化方法，解决了低秩张量恢复问题。通过将张量Schatten-p范数分解成l2,q范数与l2,1范数的加权和，避免了求解张量Schatten-p范数需要张量奇异值分解的问题，从而降低了算法的复杂度。采用交替方向乘子法用于求解提出的模型。通过真实数据的实验，在精度和时间复杂度两个方面验证了算法的有效性。
Abstract: In this paper, a new regularization method is proposed to solve the recovery problem of low rank tensors. By decomposing the tensor Schatten-p norm into the weighted sum of l2,q -norm and l2,1 -norm, the problem of solving the tensor Schatten-p norm requiring tensor singular value decom-position is avoided, reducing the complexity of the algorithm. The alternating direction multiplier method is used to solve the proposed model. Experiments on real data demonstrate the effective-ness of the algorithm in terms of accuracy and time complexity.
文章引用：李鸿燕, 姜伟. 双因子张量范数正则化低秩张量填充[J]. 应用数学进展, 2022, 11(10): 6908-6914. https://doi.org/10.12677/AAM.2022.1110732

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