L1-Norm Tucker Tensor Decomposition
L1-Norm Tucker Tensor Decomposition
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DOI：
10.1109/access.2019.2955134
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发表时间：
2019-04
期刊：
影响因子：
3.9
通讯作者：
Dimitris G. Chachlakis;Ashley Prater-Bennette;Panos P. Markopoulos
中科院分区：
文献类型：
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作者：
Dimitris G. Chachlakis;Ashley Prater-Bennette;Panos P. Markopoulos
Tucker分解是主成分分析(PCA)的标准多路推广，适用于处理张量数据。与主成分分析类似，Tucker分解已被证明对错误数据很敏感，因为它基于L2范数的公式将平方重点放在外围/外围条目上。本文研究了Tucker分解的一种基于L1范数的重构形式L1-Tucker，并给出了求解它的两个算法，即L1-范数高阶奇异值分解(L1-HOSVD)和L1-范数高阶正交迭代(L1-HOOI)。所提出的算法还伴随着复杂性和收敛分析。张量重构和分类的数值研究证实，利用所提出的算法实现的L1-Tucker分解，在处理的数据是无破坏的情况下，获得了与标准Tucker相似的性能，而对严重破坏的条目表现出了较强的抵抗能力。
Tucker decomposition is a standard multi-way generalization of Principal-Component Analysis (PCA), appropriate for processing tensor data. Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based formulation which places squared emphasis to peripheral/outlying entries. In this work, we explore L1-Tucker, an L1-norm based reformulation of Tucker decomposition, and present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The proposed algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker decomposition, implemented by means of the proposed algorithms, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.