HOSVD-Based Algorithm for Weighted Tensor Completion
HOSVD-Based Algorithm for Weighted Tensor Completion
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DOI：
10.3390/jimaging7070110
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发表时间：
2021-07-07
影响因子：
3.2
通讯作者：
Needell D
中科院分区：
文献类型：
--
作者：
Chao Z;Huang L;Needell D
矩阵补齐是指在具有低维结构（如秩）的数据矩阵中补齐缺失项的问题，已有许多卓有成效的方法和分析。张量完备化是一种张量模拟，它试图从类似的低秩类型假设中估算缺失的张量条目。在本文中，我们研究的张量完成问题时，采样模式是确定的，可能是不均匀的。我们首先提出了一个有效的加权高阶奇异值分解（HOSVD）算法的恢复底层的低秩张量从噪声观测，然后推导出一个适当的加权度量下的误差界。此外，我们的算法的效率和精度都测试使用合成和真实的数据集在数值模拟。
Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.