论文标题
张量奇异值分解的有效的随机固定精确算法
An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition
论文作者
论文摘要
现有的随机算法需要对管等级的初始估计来计算张量的奇异值分解。本文提出了一种新的随机固定定期算法，该算法对于给定的三阶张量和规定的近似误差绑定，自动找到最佳的管秩和相应的低管秩近似值。该算法基于随机投影技术，并配备了功率迭代方法，以实现更好的准确性。我们对合成和现实世界数据集进行模拟，以显示所提出的算法的效率和性能。
The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition. This paper proposes a new randomized fixedprecision algorithm which for a given third-order tensor and a prescribed approximation error bound, automatically finds an optimal tubal rank and the corresponding low tubal rank approximation. The algorithm is based on the random projection technique and equipped with the power iteration method for achieving a better accuracy. We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.
