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Performance Estimation for tensor CP decomposition with Structured Factors

Abstract : The Canonical Polyadic tensor decomposition (CPD), also known as Candecomp/Parafac, is very useful in numerous scientific disciplines. Structured CPDs, i.e. with Toeplitz, circulant, or Hankel factor matrices, are often encountered in signal processing applications. As subsequently pointed out, specialized algorithms were recently proposed for estimating the deterministic parameters of structured CP decompositions. A closed-form expression of the Cramer-Rao bound (CRB) is derived, related to the problem of estimating CPD parameters, when the observed tensor is corrupted with an additive circular i.i.d. Gaussian noise. This CRB is provided for arbitrary tensor rank and sizes. Finally, the proposed CRB expression is used to asses the statistical efficiency of the existing algorithms by means of simulation results in the cases of third-order tensors having three circulant factors on one hand, and an Hankel factor on the other hand.
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Contributor : Pierre Comon <>
Submitted on : Wednesday, October 8, 2014 - 1:11:11 PM
Last modification on : Tuesday, April 20, 2021 - 4:54:04 PM
Long-term archiving on: : Friday, January 9, 2015 - 10:55:11 AM


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  • HAL Id : hal-01072538, version 1



Maxime Boizard, Remy Boyer, Gérard Favier, Pierre Comon. Performance Estimation for tensor CP decomposition with Structured Factors. ICASSP, Apr 2015, Brisbane, Australia. ⟨hal-01072538v1⟩



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