Tensor Networks for Latent Variable Analysis: Novel Algorithms for Tensor Train Approximation

0518308 - ÚTIA 2021 RIV US eng J - Článek v odborném periodiku
Phan, A. H. - Cichocki, A. - Uschmajew, A. - Tichavský, Petr - Luta, G. … celkem 6 autorů
Tensor Networks for Latent Variable Analysis: Novel Algorithms for Tensor Train Approximation.
IEEE Transactions on Neural Networks and Learning Systems. Roč. 31, č. 11 (2020), s. 4622-4636. ISSN 2162-237X. E-ISSN 2162-2388
Grant CEP: GA ČR GA17-00902S
Institucionální podpora: RVO:67985556
Klíčová slova: Blind source separation * tensor network (TN) * image denoising * nested Tucker * tensor train (TT) decomposition * Tucker-2 (TK2) decomposition * truncated singular value decomposition (SVD)
Obor OECD: Electrical and electronic engineering
Impakt faktor: 10.451, rok: 2020
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2020/SI/tichavsky-0518308.pdf https://ieeexplore.ieee.org/document/8984730

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model that represents data as an ordered network of subtensors of order-2 or order-3 has, so far, not been widely considered in these fields, although this so-called tensor network (TN) decomposition has been long studied in quantum physics and scientific computing. In this article, we present novel algorithms and applications of TN decompositions, with a particular focus on the tensor train (TT) decomposition and its variants. The novel algorithms developed for the TT decomposition update, in an alternating way, one or several core tensors at each iteration and exhibit enhanced mathematical tractability and scalability for large-scale data tensors. For rigor, the cases of the given ranks, given approximation error, and the given error bound are all considered. The proposed algorithms provide well-balanced TT-decompositions and are tested in the classic paradigms of blind source separation from a single mixture, denoising, and feature extraction, achieving superior performance over the widely used truncated algorithms for TT decomposition.
Trvalý link: http://hdl.handle.net/11104/0303994