CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F13%3A00396775" target="_blank" >RIV/67985556:_____/13:00396775 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/TSP.2013.2269046" target="_blank" >http://dx.doi.org/10.1109/TSP.2013.2269046</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TSP.2013.2269046" target="_blank" >10.1109/TSP.2013.2269046</a>

Jazyk výsledku

angličtina

Název v původním jazyce

CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping

Popis výsledku v původním jazyce

In general, algorithms for order-3 CANDECOMP/ PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easy to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding, and they are often not applicable to higher order and relatively large scale tensors. In this paper, by exploiting the uniqueness of CPD and the relation of a tensor in Kruskal form and its unfolded tensor, we propose a fast approach to deal with this problem. Insteadof directly factorizing the high order data tensor, the method decomposes an unfolded tensor with lower order, e.g., order-3 tensor. On the basis of the order-3 estimated tensor, a structured Kruskal tensor, of the same dimension as the data tensor, is then generated, and decomposed to find the final solution using fast algorithms for the structured CPD. In addition, strategies to unfold tensors are suggested and practically verified in the paper.

Název v anglickém jazyce

CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping

Popis výsledku anglicky

In general, algorithms for order-3 CANDECOMP/ PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easy to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding, and they are often not applicable to higher order and relatively large scale tensors. In this paper, by exploiting the uniqueness of CPD and the relation of a tensor in Kruskal form and its unfolded tensor, we propose a fast approach to deal with this problem. Insteadof directly factorizing the high order data tensor, the method decomposes an unfolded tensor with lower order, e.g., order-3 tensor. On the basis of the order-3 estimated tensor, a structured Kruskal tensor, of the same dimension as the data tensor, is then generated, and decomposed to find the final solution using fast algorithms for the structured CPD. In addition, strategies to unfold tensors are suggested and practically verified in the paper.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/GA102%2F09%2F1278" target="_blank" >GA102/09/1278: Pokročilé metody slepé separace signálu a slepé dekonvoluce</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

IEEE Transactions on Signal Processing

ISSN

1053-587X

e-ISSN

—

Svazek periodika

61

Číslo periodika v rámci svazku

19

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

4847-4860

Kód UT WoS článku

000324342900017

EID výsledku v databázi Scopus

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