The low-rank tensor completion problem, which aims to recover the missing data from partially observable data. However, most of the existing tensor completion algorithms based on Tucker decomposition cannot avoid using singular value decomposition (SVD) operation to calculate the Tucker factors, so they are not suitable for the completion of large-scale data. To solve this problem, they propose a new faster tensor completion algorithm, which uses the method of random projection to project the unfolding matrix of each mode of the tensor into the low-dimensional subspace, and then obtain the Tucker factors by the orthogonal decomposition. Their method can effectively avoid the high computational cost of SVD operation. The results of the synthetic data experiments and real data experiments verify the effectiveness and feasibility of their method.

中文翻译：

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张量完成的正交随机投影

低秩张量完成问题，旨在从部分可观察的数据中恢复丢失的数据。但是，现有的大多数基于Tucker分解的张量完成算法都无法避免使用奇异值分解（SVD）运算来计算Tucker因子，因此它们不适合用于大规模数据的完成。为了解决这个问题，他们提出了一种新的更快的张量完成算法，该算法使用随机投影的方法将张量的每种模式的展开矩阵投影到低维子空间中，然后通过正交分解获得塔克因子。他们的方法可以有效避免SVD运算的高计算成本。综合数据实验和真实数据实验的结果证明了该方法的有效性和可行性。