L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis
L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis
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DOI：
10.1109/icassp40776.2020.9053701
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发表时间：
2020-05
期刊：
影响因子：
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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
标准Tucker张量分解寻求最大化压缩张量的L2范数;因此，它对处理数据中的离群/高幅度条目非常敏感。为了抵消异常值在张量数据分析中的影响，我们提出了L1-Tucker：标准Tucker分解的重新表述，通过简单地将异常响应的L2范数替换为更坚固的L1范数。然后，我们提出了L1-范数高阶正交迭代（L1-HOOI）算法的近似解的L1-Tucker。我们的数据重建和分类的数值研究证实，L1-HOOI表现出强大的抵抗离群值相比，标准的同行。
Standard Tucker tensor decomposition seeks to maximize the L2-norm of the compressed tensor; thus, it is very responsive to outlying/high-magnitude entries among the processed data. To counteract the impact of outliers in tensor data analysis, we propose L1-Tucker: a reformulation of standard Tucker decomposition, resulting by simple substitution of the outlier-responsive L2-norm by the sturdier L1-norm. Then, we propose the L1-norm Higher Order Orthogonal Iterations (L1-HOOI) algorithm for the approximate solution to L1-Tucker. Our numerical studies on data reconstruction and classification corroborate that L1-HOOI exhibits sturdy resistance against outliers compared to standard counterparts.