Non-orthogonal tensor diagonalization

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Non-orthogonal tensor diagonalization

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10103 - Statistics and probability

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

Signal Processing

ISSN

0165-1684

e-ISSN

—

Volume of the periodical

138

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

8

Pages from-to

313-320

UT code for WoS article

000401043400032

EID of the result in the Scopus database

2-s2.0-85017217771