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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Error Preserving Correction: A Method for CP Decomposition at a Target Error Bound
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA17-00902S" target="_blank" >GA17-00902S: Advanded Joint Blind Source Separation Methods</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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