论文标题
三阶张量的随机奇异值分解
A randomized singular value decomposition for third-order oriented tensors
论文作者
论文摘要
Zeng和NG提出的定向的奇异值分解（O-SVD）为基于T-产品的三阶张量奇异值分解提供了混合方法，而变换矩阵是高阶单数值分解的因子矩阵。沿着这种静脉延续，本文探索了通过张量列表1分解更有效地实现O-SVD，并给出了截断的O-SVD。由于概率算法的成功，我们开发了O-SVD的随机版本，并介绍其详细的错误分析。与当前的张量分解相比，新算法在效率方面具有优势，同时保持良好的准确性。我们的主张得到了来自实际应用的几个定向张量的数值实验的支持。
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order singular value decomposition. Continuing along this vein, this paper explores realizing the O-SVD more efficiently by the tensor-train rank-1 decomposition and gives a truncated O-SVD. Motivated by the success of probabilistic algorithms, we develop a randomized version of the O-SVD and present its detailed error analysis. The new algorithm has advantages in efficiency while keeping good accuracy compared with the current tensor decompositions. Our claims are supported by numerical experiments on several oriented tensors from real applications.
