Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some randomized algorithms have been proposed; however, they are not suitable for noisy data. The randomized block Krylov method is capable of dealing with heavy-tailed noisy data in the low-rank approximation of matrices. In this paper, we present a randomized algorithm for low-rank tensor train approximation of large-scale tensors based on randomized block Krylov subspace iteration and provide theoretical guarantees. Numerical experiments on synthetic and real-world tensor data demonstrate the effectiveness of the proposed algorithm.

翻译：张量列分解是处理高维、大规模张量数据的有力工具，其不受维度灾难的影响。为加速辅助展开矩阵的计算，已有研究者提出了若干随机算法，但这些算法不适用于含噪数据。随机块Krylov方法能够处理矩阵低秩近似中的重尾噪声数据。本文基于随机块Krylov子空间迭代，提出了一种用于大规模张量低秩张量列近似的随机算法，并给出了理论保证。在合成张量数据与真实张量数据上的数值实验验证了所提算法的有效性。