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• W2010417247 abstract "This paper presents a Cramer-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 i.i.d. 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. The expression needs less operations for computing the bound, O(NR^6), than the best existing state-of-the art algorithm, O(N^3R^6) operations, where N and R are the tensor order and the tensor rank. 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). A novel expression is derived for a Hessian matrix needed in popular damped Gauss-Newton method for solving the CP decomposition of tensors with missing elements. Beside computing the CRLB for these tensors the expression may serve for design of damped Gauss-Newton algorithm for the decomposition." @default.
• W2010417247 created "2016-06-24" @default.
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• W2010417247 date "2013-04-01" @default.
• W2010417247 modified "2023-10-17" @default.
• W2010417247 title "Cramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition" @default.
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• W2010417247 doi "https://doi.org/10.1109/tsp.2013.2245660" @default.
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