Abstract
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to harness the notorious curse of dimensionality. The main forms of tensor decomposition include CP decomposition, Tucker decomposition, tensor train (TT) decomposition, etc. Each of the existing TT decomposition algorithms, including the TT-SVD and randomized TT-SVD, is successful in the field, but neither can both accurately and efficiently decompose large-scale sparse tensors. Based on previous research, this paper proposes a new quasi-optimal fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and the upper bound of computational complexity derived. It can also efficiently produce sparse TT with no numerical error and slightly larger TT-ranks on demand. In numerical experiments, we verify that the proposed algorithm can decompose sparse tensors in a much faster speed than the TT-SVD, and have advantages on speed, precision and versatility over the randomized TT-SVD and TT-cross. And, with it we can realize large-scale sparse matrix TT decomposition that was previously unachievable, enabling the tensor decomposition based algorithms to be applied in more scenarios.
Original language | English |
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Article number | 113972 |
Number of pages | 18 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 405 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Parallel-vector rounding
- Sparse data
- Tensor train decomposition
- TT-rounding