A Further Improvement of a Fast Damped Gauss–Newton Algorithm for CANDECOMP-PARAFAC Tensor Decomposition

0392903 - ÚTIA 2014 RIV CA eng C - Konferenční příspěvek (zahraniční konf.)
Tichavský, Petr - Phan, A. H. - Cichocki, A.
A Further Improvement of a Fast Damped Gauss–Newton Algorithm for CANDECOMP-PARAFAC Tensor Decomposition.
2013 IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP 2013. Vancouver: IEEE, 2013, s. 5964-5968. ISBN 978-1-4799-0355-9.
[IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP 2013. Vancouver (CA), 27.05.2013-31.05.2013]
Grant CEP: GA ČR GA102/09/1278
Institucionální podpora: RVO:67985556
Klíčová slova: tensor factorization * Gauss-Newton method
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
http://library.utia.cas.cz/separaty/2013/SI/tichavsky-a further improvement of a fast damped gauss-newton algorithm for candecomp-parafac tensor decomposition.pdf

In this paper, a novel implementation of the damped Gauss-Newton algorithm (also known as Levenberg-Marquart) for the CANDECOMP-PARAFAC (CP) tensor decomposition is proposed. The method is based on a fast inversion of the approximate Hessian for the problem. It is shown that the inversion can be computed on O(NR^6) operations, where N and R is the tensor order and rank, respectively. It is less than in the best existing state-of-the art algorithm with O(N^3R^6) operations. The damped Gauss-Newton algorithm is suitable namely for difficult scenarios, where nearly-colinear factors appear in several modes simultaneously. Performance of the method is shown on decomposition of large tensors (100 × 100 × 100 and 100 × 100 × 100 × 100) of rank 5 to 90.
Trvalý link: http://hdl.handle.net/11104/0221812