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 HOSVD algorithm for 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.
翻译:矩阵完成后,在低维结构的数据矩阵(如等级)中完成缺失条目的问题,已经看到许多富有成效的方法和分析。Tensor的完成是模拟的,试图从类似的低级假设中估算缺失的光度条目。在本文中,当抽样模式具有确定性且可能不统一时,我们研究了单度完成问题。我们首先提出了一个高效的加权HOSVD算法,以便从噪音的观测中恢复底层的低级传感器,然后在适当加权的衡量标准下得出错误界限。此外,我们算法的效率和准确性在数字模拟中使用合成和真实数据集进行测试。