Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria
Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria
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DOI：
10.1109/tsp.2016.2620965
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发表时间：
2017-03
影响因子：
5.4
通讯作者：
Tatsuya Yokota;Namgil Lee;A. Cichocki
中科院分区：
文献类型：
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作者：
Tatsuya Yokota;Namgil Lee;A. Cichocki
当原始数据张量的秩未知且观测到的张量有噪声时，张量分解中的模型选择对于实际应用非常重要。在Tucker模型中，通过矩阵展开将最小描述长度（MDL）或贝叶斯信息准则应用于张量，但当张量具有Tucker模型给出的多线性低秩结构时，这些方法对噪声敏感。在这项研究中，我们提出了改进MDL的新方法，使其对噪声的鲁棒性更强。通过对张量“多线性低秩结构”的分析，从理论上证明了所提方法的正确性。大量的实验包括数值模拟和图像去噪的实际应用，以说明所提出的方法的优点。
Model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy. In the Tucker model, the minimum description length (MDL) or Bayesian information criteria have been applied to tensors via matrix unfolding, but these methods are sensitive to noise when the tensors have a multilinear low rank structure given by the Tucker model. In this study, we propose new methods for improving the MDL so it is more robust to noise. The proposed methods are justified theoretically by analyzing the “multilinear low-rank structure” of tensors. Extensive experiments including numerical simulations and a real application to image denoising are provided to illustrate the advantages of the proposed methods.