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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00518308" target="_blank" >RIV/67985556:_____/20:00518308 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/8984730" target="_blank" >https://ieeexplore.ieee.org/document/8984730</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TNNLS.2019.2956926" target="_blank" >10.1109/TNNLS.2019.2956926</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20201 - Electrical and electronic engineering

Projekt

<a href="/cs/project/GA17-00902S" target="_blank" >GA17-00902S: Pokročilé metody slepé separace podprostorů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Transactions on Neural Networks and Learning Systems

ISSN

2162-237X

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

4622-4636

Kód UT WoS článku

000587699700017

EID výsledku v databázi Scopus

2-s2.0-85093097685