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强大工具，不易受到维数灾难的影响。为了加速辅助展开矩阵的计算，已有学者提出了一些随机算法，但这些算法不适用于含噪声数据。随机块Krylov方法能够在矩阵的低秩逼近中处理重尾噪声数据。本文提出一种基于随机块Krylov子空间迭代的大规模张量低秩张量列近似的随机算法，并给出理论保证。在合成数据和真实张量数据上的数值实验验证了所提算法的有效性。