A Randomized Block Krylov Method for Tensor Train Approximation
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- 10.48550/arXiv.2308.01480
- arXiv:
- arXiv:2308.01480
- Bibcode:
- 2023arXiv230801480Y
- Keywords:
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- Mathematics - Numerical Analysis;
- 68W20
- E-Print:
- 23 pages, 15 figures