Tensor Deflation for CANDECOMP/PARAFAC - Part I: Alternating Subspace Update Algorithm

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00448255" target="_blank" >RIV/67985556:_____/15:00448255 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/TSP.2015.2458785" target="_blank" >http://dx.doi.org/10.1109/TSP.2015.2458785</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TSP.2015.2458785" target="_blank" >10.1109/TSP.2015.2458785</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tensor Deflation for CANDECOMP/PARAFAC - Part I: Alternating Subspace Update Algorithm

Popis výsledku v původním jazyce

CANDECOMP/PARAFAC (CP) approximates multiway data by sum of rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper, we propose a novel deflation method for the problem. When one factor matrix of a rank-CP decomposition is of full column rank, the decomposition can be performed through (R-1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank. For decomposition of order-3 tensors of size RxRxR and rank-R estimation of one rank-1 tensor has a computational cost of O(R^3) per iteration which is lower than the cost O(R^4) of the ALS algorithm for the overall CP decomposition. The method can be extended to tracking one or a few rank-one tensors of slow changes, or inspect variations of common patterns in individual datasets.

Název v anglickém jazyce

Tensor Deflation for CANDECOMP/PARAFAC - Part I: Alternating Subspace Update Algorithm

Popis výsledku anglicky

CANDECOMP/PARAFAC (CP) approximates multiway data by sum of rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper, we propose a novel deflation method for the problem. When one factor matrix of a rank-CP decomposition is of full column rank, the decomposition can be performed through (R-1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank. For decomposition of order-3 tensors of size RxRxR and rank-R estimation of one rank-1 tensor has a computational cost of O(R^3) per iteration which is lower than the cost O(R^4) of the ALS algorithm for the overall CP decomposition. The method can be extended to tracking one or a few rank-one tensors of slow changes, or inspect variations of common patterns in individual datasets.

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/GA14-13713S" target="_blank" >GA14-13713S: Metody dekompozice tenzorů a jejich aplikace</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

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

63

Číslo periodika v rámci svazku

22

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

5924-5938

Kód UT WoS článku

000362746500004

EID výsledku v databázi Scopus

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