论文标题
在近似算法上，用于正交低级张量近似
On Approximation Algorithm for Orthogonal Low-Rank Tensor Approximation
论文作者
论文摘要
这项工作的目的是填补[Yang，Siam J. Matrix肛门的空白。 Appl，41（2020），1797--1825]。在这项工作中，提出了一个近似程序，以进行正交的低级张量近似；但是，仅当正顺序因子的数量是一个时，近似下限才建立。为此，通过进一步探索问题的多线性和正交性，我们引入了修改后的近似算法。无论是确定性的还是预期的，无论有多少近期因素，都可以确定下限。此外，新算法的一个主要特征是其灵活性允许确定性或随机过程求解算法中每个潜在正交因子的关键步骤。此功能可以减少大型SVD的计算，从而使算法更有效。提供了一些数值研究来验证所提出的算法的有用性。
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound was only established when the number of orthonormal factors is one. To this end, by further exploring the multilinearity and orthogonality of the problem, we introduce a modified approximation algorithm. Approximation lower bound is established, either in deterministic or expected sense, no matter how many orthonormal factors there are. In addition, a major feature of the new algorithm is its flexibility to allow either deterministic or randomized procedures to solve a key step of each latent orthonormal factor involved in the algorithm. This feature can reduce the computation of large SVDs, making the algorithm more efficient. Some numerical studies are provided to validate the usefulness of the proposed algorithm.
