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Tensor train decomposition is a powerful tool for dealing withhigh-dimensional, large-scale tensor data, which is not suffering from thecurse of dimensionality. To accelerate the calculation of the auxiliaryunfolding matrix, some randomized algorithms have been proposed; however, theyare not suitable for noisy data. The randomized block Krylov method is capableof dealing with heavy-tailed noisy data in the low-rank approximation ofmatrices. In this paper, we present a randomized algorithm for low-rank tensortrain approximation of large-scale tensors based on randomized block Krylovsubspace iteration and provide theoretical guarantees. Numerical experiments onsynthetic and real-world tensor data demonstrate the effectiveness of theproposed algorithm.

A Randomized Block Krylov Method for Tensor Train Approximation