Stability Analysis and Fast Damped-Gauss-Newton Algorithm for INDSCALTensor Decomposition

0363806 - ÚTIA 2012 RIV FR eng C - Conference Paper (international conference)
Koldovský, Zbyněk - Tichavský, Petr - Phan, A. H.
Stability Analysis and Fast Damped-Gauss-Newton Algorithm for INDSCALTensor Decomposition.
2011 IEEE Statistical Signal Processing Workshop (SSP) Proceedings. Nice: IEEE Signal Processing Society, 2011, s. 581-584. ISBN 978-1-4577-0569-4.
[2011 IEEE Statistical Signal Processing Workshop (SSP). Nice (FR), 28.06.2011-30.06.2011]
R&D Projects: GA MŠMT 1M0572; GA ČR GA102/09/1278
Grant - others:GA ČR(CZ) GAP103/11/1947
Program: GA
Institutional research plan: CEZ:AV0Z10750506
Keywords : INDSCAL * PARAFAC * tensor decomposition
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2011/SI/tichavsky-stability analysis and fast damped-gauss-newton algorithm for indscaltensor decomposition.pdf

INDSCAL is a special case of the CANDECOMP-PARAFAC (CP) decomposition of three or more-way tensors, where two factor matrices are equal. This paper provides a stability analysis of INDSCAL that is done by deriving the Cram'er-Rao lower bound (CRLB) on variance of an unbiased estimate of the tensor parameters from its noisy observation (the tensor plus a Gaussian random tensor). The existence of the bound reveals necessary conditions for the essential uniqueness of the INDSCAL decomposition. This is compared with previous results on CP. Next, analytical expressions for the inverse of the Hessian matrix, which is needed to compute the CRLB, are used in a damped Gaussian (Levenberg-Marquardt) algorithm, which gives a novel method for INDSCAL having a lower computational complexity.
Permanent Link: http://hdl.handle.net/11104/0199463