Institute of Information Theory and Automation

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Bibliography

Journal Article

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

Tichavský Petr, Phan A. H., Koldovský Zbyněk

: IEEE Transactions on Signal Processing vol.61, 8 (2013), p. 1986-1997

: GA102/09/1278, GA ČR, GAP103/11/1947, GA ČR

: Canonical polyadic decomposition, multilinear models, stability

: 10.1109/TSP.2013.2245660

: http://library.utia.cas.cz/separaty/2013/SI/tichavsky-0391438.pdf

(eng): 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).

: BB

2019-01-07 08:39