0500107 20240111141013.820190118235959.9 85058883993 000455721400005 10.1109/TSP.2018.2887192 16 s. P cav_un_epca*02567271053-587X675 (2019)1175-1190 Canonical polyadic decomposition parallel factor analysis tensor decomposition cav_un_auth*0274170 Phan A. H. JP cav_un_auth*0101212 Tichavský Petr Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0274171 Cichocki A. JP http://library.utia.cas.cz/separaty/2019/SI/tichavsky-0500107.pdf 3.1 MB https://ieeexplore.ieee.org/document/8579207 GA17-00902S GA ČR cav_un_auth*0345929 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. WOS BB 10000 10100 10103 2020 3 4 A hod 4ah 20231122143746.2 RVO:67985556 http://hdl.handle.net/11104/0293323 1 Department of Stochastic Informatics UTIA-B 20201 ENGINEERING, ELECTRICAL & ELECTRONIC S 1 Article Materials Science Multidisciplinary|Physics Applied C ENGINEERING.ELECTRICAL&ELECTRONIC 5.217 0.871 8.7 0.05234 1.718 37840 314 2.098 43.38 6.59 9616 Q1 4.385 458 Q1 91.914 86.7 Q1* Q1* 1.73 Q1 86.654 2019 Soubory v repozitáři: tichavsky-0500107.pdf 85058883993 SCOPUS PUBMED 000455721400005 WOS 3.1 MB cav_un_epca*0256727 IEEE Transactions on Signal Processing 1053-587X 1941-0476 Roč. 67 č. 5 2019 1175 1190