0391438 20240111140829.420130404235959.9 000317398500010 84875651157 10.1109/TSP.2013.2245660 12 s. P cav_un_epca*02567271053-587X618 (2013)1986-1997 Canonical polyadic decomposition multilinear models stability 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*0108100 Koldovský Zbyněk Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/SI/tichavsky-0391438.pdf 3MB GA102/09/1278 GA ČR cav_un_auth*0253174 GAP103/11/1947 GA ČR CZ cav_un_auth*0301478 This paper presents a Cramér-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a random Gaussian-distributed tensor). A novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor of an arbitrary dimension. Insightful expressions are derived for tensors of rank 1 and rank 2 of arbitrary dimension and for tensors of arbitrary dimension and rank, where two factor matrices have orthogonal columns. The results can be used as a gauge of performance of different approximate CP decomposition algorithms, prediction of their accuracy, and for checking stability of a given decomposition of a tensor (condition whether the CRLB is finite or not). 2014 BB 3 4 A 4a 20231122135558.1 RVO:67985556 http://hdl.handle.net/11104/0220515 ENGINEERINGELECTRICALELECTRONIC 3.592 0.439 7.II 0.07199 1.62 22913 508 2.074 Q1 94.605 90.927 Q1* Q1* 2013 Soubory v repozitáři: tichavsky-0391438.pdf 84875651157 SCOPUS 000317398500010 WOS 3MB cav_un_epca*0256727 IEEE Transactions on Signal Processing 1053-587X 1941-0476 Roč. 61 č. 8 2013 1986 1997