0474387 20240103214032.420170505235959.9 85017217771 000401043400032 10.1016/j.sigpro.2017.04.001 8 s. cav_un_epca*02550760165-16841381 (2017)313-320Elsevier multilinear models canonical polyadic decomposition parallel factor analysis 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*0274170 Phan A. H. JP cav_un_auth*0274171 Cichocki A. JP http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0474387.pdf cav_un_auth*0303443 GA14-13713S GA ČR CZ cav_un_auth*0345929 GA17-00902S GA ČR Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetric diagonalization of an order-three tensor, (2) a similar algorithm for a non-symmetric AJD, also called a two-sided diagonalization of an order-three tensor, and (3) an algorithm for three-sided diagonalization of order-three or order-four tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and in certain scenarios they can outperform traditional CP decomposition methods. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to tensor block-term decomposition. The proposed algorithm can either outperform the existing block-term decomposition algorithms, or produce good initial points for their application. BB 10000 10100 10103 2018 3 RVO:67985556 http://hdl.handle.net/11104/0271454 S 2 Article Engineering Electrical Electronic 2 Article Engineering Electrical Electronic 2 Article Engineering Electrical Electronic ENGINEERING.ELECTRICAL&ELECTRONIC 3.180 1.157 5.9 0.01942 0.817 11626 0.940 2.973 356 Q1 63.612 80.6 Q2 Q1 1.27 Q1 80.577 2017 85017217771 SCOPUS PUBMED 000401043400032 WOS cav_un_epca*0255076 Signal Processing 0165-1684 1872-7557 Roč. 138 č. 1 2017 313 320 Elsevier