Title :
Performance estimation for tensor CP decomposition with structured factors
Author :
Boizard, Maxime ; Boyer, Remy ; Favier, Gerard ; Cohen, Jeremy E. ; Comon, Pierre
Author_Institution :
Univ. Paris-Sud, Paris, France
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 Cramér-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.
Keywords :
Gaussian noise; matrix decomposition; statistical analysis; tensors; CPD parameter estimation; CRB; Cramer-Rao bound; Gaussian noise; additive circular; arbitrary tensor rank; arbitrary tensor sizes; canonical polyadic tensor decomposition; deterministic parameter estimation; signal processing applications; statistical efficiency assessment; structured CP decomposition; structured factors; tensor CP decomposition; Cramér-Rao bound; Multilinear Algebra; Performance Analysis; Structured matrix; Tensor Decomposition;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on
Conference_Location :
South Brisbane, QLD
DOI :
10.1109/ICASSP.2015.7178618