论文标题
基于HOSVD的算法，用于加权张量完成
HOSVD-Based Algorithm for Weighted Tensor Completion
论文作者
论文摘要
矩阵完成是在具有低维结构（例如等级）数据矩阵中完成缺失条目的问题，已经看到了许多富有成果的方法和分析。张量的完成是张量类似物，它试图从类似的低级别类型假设中估算缺失的张量条目。在本文中，我们研究了采样模式确定性且可能不均匀时的张量完成问题。我们首先提出了一种有效的加权HOSVD算法，用于从嘈杂的观测值中恢复潜在的低级别张量，然后在适当加权的度量下得出误差界限。另外，在数值模拟中，使用合成和真实数据集测试了我们算法的效率和准确性。
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.
