0448255 20240103210755.420151022235959.9 84944696619 000362746500004 10.1109/TSP.2015.2458785 15 s. P cav_un_epca*02567271053-587X6322 (2015)5924-5938 Canonical polyadic decomposition tensor deflation tensor tracking cav_un_auth*0274170 Phan A. H. JP cav_un_auth*0101212 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics Tichavský Petr UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0274171 Cichocki A. JP http://library.utia.cas.cz/separaty/2015/SI/tichavsky-0448255.pdf cav_un_auth*0303443 GA14-13713S GA ČR CZ 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. BB 2016 3 4 A hod 4ah 20231122141206.8 RVO:67985556 http://hdl.handle.net/11104/0250564 1 Department of Stochastic Informatics UTIA-B 20201 ENGINEERING, ELECTRICAL & ELECTRONIC S ENGINEERING.ELECTRICAL&ELECTRONIC 3.157 0.462 7.8 0.0625 1.527 22917 1.581 Q1 2.134 496 Q1 89.565 87 Q1 Q1* 86.965 2015 Soubory v repozitáři: tichavsky-0448255.pdf 84944696619 SCOPUS 000362746500004 WOS cav_un_epca*0256727 IEEE Transactions on Signal Processing 1053-587X 1941-0476 Roč. 63 č. 22 2015 5924 5938