Non-orthogonal tensor diagonalization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00474387" target="_blank" >RIV/67985556:_____/17:00474387 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.sigpro.2017.04.001" target="_blank" >http://dx.doi.org/10.1016/j.sigpro.2017.04.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.sigpro.2017.04.001" target="_blank" >10.1016/j.sigpro.2017.04.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-orthogonal tensor diagonalization

Popis výsledku v původním jazyce

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions ofnthe tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetricndiagonalization of an order-three tensor, (2) a similar algorithm for a non-symmetric AJD, also called a two-sided diagonalization of an order-three tensor, and (3) an algorithm for three-sidedndiagonalization of order-three or order-four tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and in certain scenarios they can outperformntraditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithmncan either outperform the existing block-term decomposition algorithms, or produce good initial points for their application.

Název v anglickém jazyce

Non-orthogonal tensor diagonalization

Popis výsledku anglicky

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions ofnthe tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetricndiagonalization of an order-three tensor, (2) a similar algorithm for a non-symmetric AJD, also called a two-sided diagonalization of an order-three tensor, and (3) an algorithm for three-sidedndiagonalization of order-three or order-four tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and in certain scenarios they can outperformntraditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithmncan either outperform the existing block-term decomposition algorithms, or produce good initial points for their application.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Signal Processing

ISSN

0165-1684

e-ISSN

—

Svazek periodika

138

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

313-320

Kód UT WoS článku

000401043400032

EID výsledku v databázi Scopus

2-s2.0-85017217771