Error Preserving Correction: A Method for CP Decomposition at a Target Error Bound

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F19%3A00500107" target="_blank" >RIV/67985556:_____/19:00500107 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/8579207" target="_blank" >https://ieeexplore.ieee.org/document/8579207</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TSP.2018.2887192" target="_blank" >10.1109/TSP.2018.2887192</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Error Preserving Correction: A Method for CP Decomposition at a Target Error Bound

Popis výsledku v původním jazyce

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, especially, when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does not have an optimal solution. In such cases, norms of some rank-1 tensors become significantly large and cancel each other. This makes algorithms getting stuck in local minima while running a huge number of iterations does not improve the decomposition. In this paper, we propose an error preservation correction method to deal with such problem. Our aim is to seek an alternative tensor, which preserves the approximation error, but norms of rank-1 tensor components of the new tensor are minimized. Alternating and all-at-once correction algorithms have been developed for the problem. In addition, we propose a novel CPD with a bound constraint on the norm of the rank-one tensors. The method can be useful for decomposing tensors that cannot be performed by traditional algorithms. Finally, we demonstrate an application of the proposed method in image denoising and decomposition of the weight tensors in convolutional neural networks.

Název v anglickém jazyce

Error Preserving Correction: A Method for CP Decomposition at a Target Error Bound

Popis výsledku anglicky

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, especially, when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does not have an optimal solution. In such cases, norms of some rank-1 tensors become significantly large and cancel each other. This makes algorithms getting stuck in local minima while running a huge number of iterations does not improve the decomposition. In this paper, we propose an error preservation correction method to deal with such problem. Our aim is to seek an alternative tensor, which preserves the approximation error, but norms of rank-1 tensor components of the new tensor are minimized. Alternating and all-at-once correction algorithms have been developed for the problem. In addition, we propose a novel CPD with a bound constraint on the norm of the rank-one tensors. The method can be useful for decomposing tensors that cannot be performed by traditional algorithms. Finally, we demonstrate an application of the proposed method in image denoising and decomposition of the weight tensors in convolutional neural networks.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

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

2019

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

67

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

1175-1190

Kód UT WoS článku

000455721400005

EID výsledku v databázi Scopus

2-s2.0-85058883993