Cramér-Rao-Induced Bounds for CANDECOMP/ PARAFAC Tensor Decomposition

0391438 - ÚTIA 2014 RIV US eng J - Článek v odborném periodiku
Tichavský, Petr - Phan, A. H. - Koldovský, Zbyněk
Cramér-Rao-Induced Bounds for CANDECOMP/ PARAFAC Tensor Decomposition.
IEEE Transactions on Signal Processing. Roč. 61, č. 8 (2013), s. 1986-1997. ISSN 1053-587X. E-ISSN 1941-0476
Grant CEP: GA ČR GA102/09/1278
Grant ostatní: GA ČR(CZ) GAP103/11/1947
Program: GA
Institucionální podpora: RVO:67985556
Klíčová slova: Canonical polyadic decomposition * multilinear models * stability
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
Impakt faktor: 3.198, rok: 2013
http://library.utia.cas.cz/separaty/2013/SI/tichavsky-0391438.pdf

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).
Trvalý link: http://hdl.handle.net/11104/0220515