基于Lq范数的稀疏张量分解问题
Sparse Tensor Decomposition Based on Lq Norm
DOI: 10.12677/AAM.2020.93036, PDF,   
作者: 姜 玉：广西大学数学与信息科学学院，广西 南宁
关键词: 稀疏性；张量分解；乘子交替方向法；Sparsity； Tensor Decomposition； Alternating Direction of Method of Multipliers
摘要: 在张量分解中，稀疏性的引入解决了实际应用中遇到的一些困难，本文简单的介绍了张量及张量CP分解的相关概念，在已有研究的基础上提出基于Lq范数(0 < q < 1)的稀疏张量分解问题，并使用乘子交替方向法来进行求解，以及给出q=1/2时问题解的形式。
Abstract: Sparsity in tensor decomposition has solved some difficulties encountered in actual application. This paper simply introduces related concepts of tensor and CP (CANDECOMP/PARAFAC) decom-position. Then, we propose the decomposition based on Lq norm (0 < q < 1), and solve it by Alter-nating Direction of Method of Multipliers. This paper also gives an explicit solution when q=1/2.
文章引用：姜玉. 基于Lq范数的稀疏张量分解问题[J]. 应用数学进展, 2020, 9(3): 301-306. https://doi.org/10.12677/AAM.2020.93036

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